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Tests of general relativity serve to establish observational evidence for the
theory of general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. G ...
. The first three tests, proposed by
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
in 1915, concerned the "anomalous"
precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...
of the
perihelion An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any ellip ...
of
Mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...
, the bending of light in
gravitational field In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational phenome ...
s, and the
gravitational redshift In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy ...
. The precession of Mercury was already known; experiments showing light bending in accordance with the predictions of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
were performed in 1919, with increasingly precise measurements made in subsequent tests; and scientists claimed to have measured the gravitational redshift in 1925, although measurements sensitive enough to actually confirm the theory were not made until 1954. A more accurate program starting in 1959 tested general relativity in the weak gravitational field limit, severely limiting possible deviations from the theory. In the 1970s, scientists began to make additional tests, starting with Irwin Shapiro's measurement of the relativistic time delay in radar signal travel time near the sun. Beginning in 1974, Hulse,
Taylor Taylor, Taylors or Taylor's may refer to: People * Taylor (surname) ** List of people with surname Taylor * Taylor (given name), including Tayla and Taylah * Taylor sept, a branch of Scottish clan Cameron * Justice Taylor (disambiguation) Pl ...
and others studied the behaviour of
binary pulsar A binary pulsar is a pulsar with a binary companion, often a white dwarf or neutron star. (In at least one case, the double pulsar PSR J0737-3039, the companion neutron star is another pulsar as well.) Binary pulsars are one of the few objects ...
s experiencing much stronger gravitational fields than those found in the Solar System. Both in the weak field limit (as in the Solar System) and with the stronger fields present in systems of binary pulsars the predictions of general relativity have been extremely well tested. In February 2016, the
Advanced LIGO The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Two large ...
team announced that they had directly detected gravitational waves from a black hole merger. This discovery, along with additional detections announced in June 2016 and June 2017,Conover, Emily
LIGO snags another set of gravitational waves
''Science News'', June 1, 2017. Retrieved 8 June 2017.
tested general relativity in the very strong field limit, observing to date no deviations from theory.


Classical tests

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
proposed three tests of general relativity, subsequently called the "classical tests" of general relativity, in 1916: # the perihelion precession of
Mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...
's orbit # the deflection of light by the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
# the
gravitational redshift In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy ...
of light In the letter to ''
The Times ''The Times'' is a British daily national newspaper based in London. It began in 1785 under the title ''The Daily Universal Register'', adopting its current name on 1 January 1788. ''The Times'' and its sister paper ''The Sunday Times'' (fou ...
'' (of London) on November 28, 1919, he described the theory of relativity and thanked his English colleagues for their understanding and testing of his work. He also mentioned three classical tests with comments: :"The chief attraction of the theory lies in its logical completeness. If a single one of the conclusions drawn from it proves wrong, it must be given up; to modify it without destroying the whole structure seems to be impossible."


Perihelion precession of Mercury

Under
Newtonian physics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mec ...
, an object in an (isolated) two-body system, consisting of the object orbiting a spherical mass, would trace out an
ellipse In mathematics, an ellipse is a plane curve surrounding two focus (geometry), focal points, such that for all points on the curve, the sum of the two distances to the focal points is a constant. It generalizes a circle, which is the special ty ...
with the center of mass of the system at a
focus Focus, or its plural form foci may refer to: Arts * Focus or Focus Festival, former name of the Adelaide Fringe arts festival in South Australia Film *''Focus'', a 1962 TV film starring James Whitmore * ''Focus'' (2001 film), a 2001 film based ...
of the ellipse. The point of closest approach, called the
periapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary (astronomy), primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two ...
(or when the central body is the Sun,
perihelion An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two apsides in any ellip ...
), is fixed. Hence the major axis of the ellipse remains fixed in space. Both objects orbit around the center of mass of this system, so they each have their own ellipse. However, a number of effects in the Solar System cause the perihelia of planets to precess (rotate) around the Sun, or equivalently, cause the major axis to rotate about the center of mass, hence changing its orientation in space. The principal cause is the presence of other planets which
perturb Perturbation or perturb may refer to: * Perturbation theory, mathematical methods that give approximate solutions to problems that cannot be solved exactly * Perturbation (geology), changes in the nature of alluvial deposits over time * Perturbatio ...
one another's orbit. Another (much less significant) effect is solar oblateness.
Mercury Mercury commonly refers to: * Mercury (planet), the nearest planet to the Sun * Mercury (element), a metallic chemical element with the symbol Hg * Mercury (mythology), a Roman god Mercury or The Mercury may also refer to: Companies * Merc ...
deviates from the precession predicted from these Newtonian effects. This anomalous rate of precession of the perihelion of Mercury's orbit was first recognized in 1859 as a problem in
celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...
, by
Urbain Le Verrier Urbain Jean Joseph Le Verrier FRS (FOR) HFRSE (; 11 March 1811 – 23 September 1877) was a French astronomer and mathematician who specialized in celestial mechanics and is best known for predicting the existence and position of Neptune using ...
. His re-analysis of available timed observations of transits of Mercury over the Sun's disk from 1697 to 1848 showed that the actual rate of the precession disagreed from that predicted from Newton's theory by 38″ (
arcseconds A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
) per tropical century (later re-estimated at 43″ by
Simon Newcomb Simon Newcomb (March 12, 1835 – July 11, 1909) was a Canadian–American astronomer, applied mathematician, and autodidactic polymath. He served as Professor of Mathematics in the United States Navy and at Johns Hopkins University. Born in Nov ...
in 1882). A number of ''ad hoc'' and ultimately unsuccessful solutions were proposed, but they tended to introduce more problems. Le Verrier suggested that another hypothetical planet might exist to account for Mercury's behavior. The previously successful search for Neptune based on its perturbations of the orbit of Uranus led astronomers to place some faith in this possible explanation, and the hypothetical planet was even named
Vulcan Vulcan may refer to: Mythology * Vulcan (mythology), the god of fire, volcanoes, metalworking, and the forge in Roman mythology Arts, entertainment and media Film and television * Vulcan (''Star Trek''), name of a fictional race and their home p ...
. Finally, in 1908,
W. W. Campbell William Wallace Campbell (April 11, 1862 – June 14, 1938) was an American astronomer, and director of Lick Observatory from 1901 to 1930. He specialized in spectroscopy. He was the tenth president of the University of California from 1923 to ...
, Director of the Lick Observatory, after the comprehensive photographic observations by Lick astronomer, Charles D. Perrine, at three solar eclipse expeditions, stated, “In my opinion, Dr. Perrine’s work at the three eclipses of 1901, 1905, and 1908 brings the observational side of the famous intramercurial-planet problem definitely to a close.” Subsequently, no evidence of Vulcan was found and Einstein's 1915 general theory accounted for Mercury's anomalous precession. Einstein wrote to Michael Besso, "Perihelion motions explained quantitatively...you will be astonished". In general relativity, this remaining
precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...
, or change of orientation of the orbital ellipse within its orbital plane, is explained by gravitation being mediated by the curvature of spacetime. Einstein showed that general relativity agrees closely with the observed amount of perihelion shift. This was a powerful factor motivating the adoption of general relativity. Although earlier measurements of planetary orbits were made using conventional telescopes, more accurate measurements are now made with
radar Radar is a detection system that uses radio waves to determine the distance (''ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, w ...
. The total observed precession of Mercury is 574.10″±0.65 per century relative to the inertial ICRF. This precession can be attributed to the following causes: The correction by 42.980±0.001″/cy is the prediction of post-Newtonian theory with
parameters A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...
\gamma = \beta = 1. Thus the effect can be fully explained by general relativity. More recent calculations based on more precise measurements have not materially changed the situation. In general relativity the perihelion shift ''σ'', expressed in radians per revolution, is approximately given by: :\sigma = \frac \ , where ''L'' is the
semi-major axis In geometry, the major axis of an ellipse is its longest diameter: a line segment that runs through the center and both foci, with ends at the two most widely separated points of the perimeter. The semi-major axis (major semiaxis) is the long ...
, ''T'' is the
orbital period The orbital period (also revolution period) is the amount of time a given astronomical object takes to complete one orbit around another object. In astronomy, it usually applies to planets or asteroids orbiting the Sun, moons orbiting planets ...
, ''c'' is the speed of light, and ''e'' is the
orbital eccentricity In astrodynamics, the orbital eccentricity of an astronomical object is a dimensionless parameter that determines the amount by which its orbit around another body deviates from a perfect circle. A value of 0 is a circular orbit, values betwee ...
(see:
Two-body problem in general relativity The two-body problem in general relativity is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler problem is essential to calculate the bending of lig ...
). The other planets experience perihelion shifts as well, but, since they are farther from the Sun and have longer periods, their shifts are lower, and could not be observed accurately until long after Mercury's. For example, the perihelion shift of Earth's orbit due to general relativity is theoretically 3.83868" per century and experimentally 3.8387±0.0004"/cy, Venus's is 8.62473"/cy and 8.6247±0.0005″/cy and Mars' is 1.351±0.001"/cy. Both values have now been measured, with results in good agreement with theory. The
periapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary (astronomy), primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two ...
shift has also now been measured for binary pulsar systems, with
PSR 1913+16 PSR may refer to: Organizations * Pacific School of Religion, Berkeley, California, US * Palestinian Center for Policy and Survey Research * Physicians for Social Responsibility, US ;Political parties: * Revolutionary Socialist Party (Portugal) ( ...
amounting to 4.2° per year. These observations are consistent with general relativity. It is also possible to measure periapsis shift in binary star systems which do not contain ultra-dense stars, but it is more difficult to model the classical effects precisely – for example, the alignment of the stars' spin to their orbital plane needs to be known and is hard to measure directly. A few systems, such as DI Herculis,Naeye, Robert
"Stellar Mystery Solved, Einstein Safe"
''Sky and Telescope'', September 16, 2009. See als
MIT Press Release
September 17, 2009. Accessed 8 June 2017.
have been measured as test cases for general relativity.


Deflection of light by the Sun

Henry Cavendish Henry Cavendish ( ; 10 October 1731 – 24 February 1810) was an English natural philosopher and scientist who was an important experimental and theoretical chemist and physicist. He is noted for his discovery of hydrogen, which he termed "infl ...
in 1784 (in an unpublished manuscript) and Johann Georg von Soldner in 1801 (published in 1804) had pointed out that Newtonian gravity predicts that starlight will bend around a massive object. The same value as Soldner's was calculated by Einstein in 1911 based on the equivalence principle alone. However, Einstein noted in 1915 in the process of completing general relativity, that his 1911 result (and thus Soldner's 1801 result) is only half of the correct value. Einstein became the first to calculate the correct value for light bending: 1.75
arcsecond A minute of arc, arcminute (arcmin), arc minute, or minute arc, denoted by the symbol , is a unit of angular measurement equal to of one degree. Since one degree is of a turn (or complete rotation), one minute of arc is of a turn. The na ...
s for light that grazes the Sun. The first observation of light deflection was performed by noting the change in position of
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s as they passed near the Sun on the
celestial sphere In astronomy and navigation, the celestial sphere is an abstract sphere that has an arbitrarily large radius and is concentric to Earth. All objects in the sky can be conceived as being projected upon the inner surface of the celestial sphere, ...
. The observations were performed by
Arthur Eddington Sir Arthur Stanley Eddington (28 December 1882 – 22 November 1944) was an English astronomer, physicist, and mathematician. He was also a philosopher of science and a populariser of science. The Eddington limit, the natural limit to the lumin ...
and his collaborators (see
Eddington experiment The Eddington experiment was an observational test of general relativity, organised by the British astronomers Frank Watson Dyson and Arthur Stanley Eddington in 1919. The observations were of the Solar eclipse of May 29, 1919, total solar eclip ...
) during the total
solar eclipse of May 29, 1919 A total solar eclipse occurred on Thursday, May 29, 1919. With the duration of totality at maximum eclipse of 6 minutes 50.75 seconds, it was the longest solar eclipse since May 27, 1416. A longer total solar eclipse would later occur on June 8 ...
, when the stars near the Sun (at that time in the constellation
Taurus Taurus is Latin for 'bull' and may refer to: * Taurus (astrology), the astrological sign * Taurus (constellation), one of the constellations of the zodiac * Taurus (mythology), one of two Greek mythological characters named Taurus * '' Bos tauru ...
) could be observed. Observations were made simultaneously in the cities of
Sobral, Ceará Sobral is a municipality in the state of Ceará, Brazil. Sobral is the fifth largest municipality of Ceará, after Fortaleza. Its economy is based on agriculture, services and some manufacturing industries. The city has two public universitie ...
, Brazil and in
São Tomé and Príncipe São Tomé and Príncipe (; pt, São Tomé e Príncipe (); English: " Saint Thomas and Prince"), officially the Democratic Republic of São Tomé and Príncipe ( pt, República Democrática de São Tomé e Príncipe), is a Portuguese-speaking i ...
on the west coast of Africa. The result was considered spectacular news and made the front page of most major newspapers. It made Einstein and his theory of general relativity world-famous. When asked by his assistant what his reaction would have been if general relativity had not been confirmed by Eddington and Dyson in 1919, Einstein famously made the quip: "Then I would feel sorry for the dear Lord. The theory is correct anyway." The early accuracy, however, was poor and there was doubt that the small number of measured star locations and instrument questions could produce a reliable result. The results were argued by some to have been plagued by
systematic error Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a " mistak ...
and possibly
confirmation bias Confirmation bias is the tendency to search for, interpret, favor, and recall information in a way that confirms or supports one's prior beliefs or values. People display this bias when they select information that supports their views, ignoring ...
, although modern reanalysis of the dataset suggests that Eddington's analysis was accurate.D. Kennefick, "Testing relativity from the 1919 eclipse- a question of bias", ''Physics Today'', March 2009, pp. 37–42. The measurement was repeated by a team from the
Lick Observatory The Lick Observatory is an astronomical observatory owned and operated by the University of California. It is on the summit of Mount Hamilton, in the Diablo Range just east of San Jose, California, United States. The observatory is managed by th ...
led by the Director
W. W. Campbell William Wallace Campbell (April 11, 1862 – June 14, 1938) was an American astronomer, and director of Lick Observatory from 1901 to 1930. He specialized in spectroscopy. He was the tenth president of the University of California from 1923 to ...
in the 1922 eclipse as observed in remote Australian station of
Wallal Wallal is the location of a bore in the Kimberley region of Western Australia. The bore is located from the Great Northern Highway between Port Hedland and Broome and has an elevation of . The nearest town is Marble Bar, south of the bor ...
, with results based on hundreds of star positions that agreed with the 1919 results and has been repeated several times since, most notably in 1953 by
Yerkes Observatory Yerkes Observatory ( ) is an astronomical observatory located in Williams Bay, Wisconsin, United States. The observatory was operated by the University of Chicago Department of Astronomy and Astrophysics from its founding in 1897 to 2018. Owne ...
astronomers and in 1973 by a team from the
University of Texas The University of Texas at Austin (UT Austin, UT, or Texas) is a public research university in Austin, Texas. It was founded in 1883 and is the oldest institution in the University of Texas System. With 40,916 undergraduate students, 11,075 ...
. Considerable uncertainty remained in these measurements for almost fifty years, until observations started being made at
radio frequencies Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the upper ...
. The deflection of starlight by the nearby
white dwarf A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes fro ...
star Stein 2051 B has also been measured.


Gravitational redshift of light

Einstein predicted the
gravitational redshift In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy ...
of light from the
equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
in 1907, and it was predicted that this effect might be measured in the spectral lines of a
white dwarf star A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes f ...
, which has a very high gravitational field. Initial attempts to measure the gravitational redshift of the spectrum of Sirius-B, were done by
Walter Sydney Adams Walter Sydney Adams (December 20, 1876 – May 11, 1956) was an American astronomer. Life and work Adams was born in Antioch, Turkey, to Lucien Harper Adams and Nancy Dorrance Francis Adams, missionary parents, and was brought to the U.S. i ...
in 1925, but the result was criticized as being unusable due to the contamination from light from the (much brighter) primary star,
Sirius Sirius is the list of brightest stars, brightest star in the night sky. Its name is derived from the Ancient Greek language, Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinisation ...
.Hetherington, N. S.
"Sirius B and the gravitational redshift – an historical review"
''Quarterly Journal Royal Astronomical Society, vol. 21,'' Sept. 1980, p. 246-252. Accessed 6 April 2017.
Holberg, J. B.

''Journal for the History of Astronomy, Vol. 41,'' 1, 2010, p. 41-64. Accessed 6 April 2017.
The first accurate measurement of the gravitational redshift of a white dwarf was done by Popper in 1954, measuring a 21 km/s gravitational redshift of 40 Eridani B. The redshift of Sirius B was finally measured by Greenstein ''et al.'' in 1971, obtaining the value for the gravitational redshift of 89±16 km/s, with more accurate measurements by the Hubble Space Telescope showing 80.4±4.8 km/s.


Tests of special relativity

The general theory of relativity incorporates Einstein's
special theory of relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between Spacetime, space and time. In Albert Einstein's original treatment, the theory is based on two Postulates of ...
, and hence tests of special relativity are also testing aspects of general relativity. As a consequence of the
equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
,
Lorentz invariance In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
holds locally in non-rotating, freely falling reference frames. Experiments related to Lorentz invariance special relativity (that is, when gravitational effects can be neglected) are described in
tests of special relativity Special relativity is a physical theory that plays a fundamental role in the description of all physical phenomena, as long as gravitation is not significant. Many experiments played (and still play) an important role in its development and justific ...
.


Modern tests

The modern era of testing general relativity was ushered in largely at the impetus of Dicke and Schiff who laid out a framework for testing general relativity. They emphasized the importance not only of the classical tests, but of null experiments, testing for effects which in principle could occur in a theory of gravitation, but do not occur in general relativity. Other important theoretical developments included the inception of alternative theories to general relativity, in particular, scalar–tensor theories such as the Brans–Dicke theory; the
parameterized post-Newtonian formalism In physics, precisely in the study of the theory of general relativity and many alternatives to it, the post-Newtonian formalism is a calculational tool that expresses Einstein's (nonlinear) equations of gravity in terms of the lowest-order devi ...
in which deviations from general relativity can be quantified; and the framework of the
equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
. Experimentally, new developments in
space exploration Space exploration is the use of astronomy and space technology to explore outer space. While the exploration of space is carried out mainly by astronomers with telescopes, its physical exploration though is conducted both by robotic spacec ...
,
electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
and
condensed matter physics Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter, especially the solid and liquid phases which arise from electromagnetic forces between atoms. More generally, the sub ...
have made additional precise experiments possible, such as the Pound–Rebka experiment, laser interferometry and lunar rangefinding.


Post-Newtonian tests of gravity

Early tests of general relativity were hampered by the lack of viable competitors to the theory: it was not clear what sorts of tests would distinguish it from its competitors. General relativity was the only known relativistic theory of gravity compatible with special relativity and observations. Moreover, it is an extremely simple and elegant theory. This changed with the introduction of Brans–Dicke theory in 1960. This theory is arguably simpler, as it contains no
dimensionful In engineering and science, dimensional analysis is the analysis of the relationships between different physical quantities by identifying their base quantity, base quantities (such as length, mass, time, and electric current) and units of measur ...
constants, and is compatible with a version of
Mach's principle In theoretical physics, particularly in discussions of gravitation theories, Mach's principle (or Mach's conjecture) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The hypothe ...
and Dirac's large numbers hypothesis, two philosophical ideas which have been influential in the history of relativity. Ultimately, this led to the development of the parametrized post-Newtonian formalism by Nordtvedt and
Will Will may refer to: Common meanings * Will and testament, instructions for the disposition of one's property after death * Will (philosophy), or willpower * Will (sociology) * Will, volition (psychology) * Will, a modal verb - see Shall and will ...
, which parametrizes, in terms of ten adjustable parameters, all the possible departures from Newton's law of universal gravitation to first order in the velocity of moving objects (''i.e.'' to first order in v/c, where ''v'' is the velocity of an object and ''c'' is the speed of light). This approximation allows the possible deviations from general relativity, for slowly moving objects in weak gravitational fields, to be systematically analyzed. Much effort has been put into constraining the post-Newtonian parameters, and deviations from general relativity are at present severely limited. The experiments testing gravitational lensing and light time delay limits the same post-Newtonian parameter, the so-called Eddington parameter γ, which is a straightforward parametrization of the amount of deflection of light by a gravitational source. It is equal to one for general relativity, and takes different values in other theories (such as Brans–Dicke theory). It is the best constrained of the ten post-Newtonian parameters, but there are other experiments designed to constrain the others. Precise observations of the perihelion shift of Mercury constrain other parameters, as do tests of the strong equivalence principle. One of the goals of the
BepiColombo BepiColombo is a joint mission of the European Space Agency (ESA) and the Japan Aerospace Exploration Agency (JAXA) to the planet Mercury. The mission comprises two satellites launched together: the Mercury Planetary Orbiter (MPO) and ''Mio'' ...
mission to Mercury, is to test the general relativity theory by measuring the parameters gamma and beta of the parametrized post-Newtonian formalism with high accuracy. The experiment is part of the Mercury Orbiter Radio science Experiment (MORE). The spacecraft was launched in October 2018 and is expected to enter orbit around Mercury in December 2025.


Gravitational lensing

One of the most important tests is
gravitational lensing A gravitational lens is a distribution of matter (such as a galaxy cluster, cluster of galaxies) between a distant light source and an observer that is capable of bending the light from the source as the light travels toward the observer. This ...
. It has been observed in distant astrophysical sources, but these are poorly controlled and it is uncertain how they constrain general relativity. The most precise tests are analogous to Eddington's 1919 experiment: they measure the deflection of radiation from a distant source by the Sun. The sources that can be most precisely analyzed are distant
radio sources An astronomical radio source is an object in outer space that emits strong radio waves. Radio emission comes from a wide variety of sources. Such objects are among the most extreme and energetic physical processes in the universe. History In 1932 ...
. In particular, some
quasar A quasar is an extremely Luminosity, luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a m ...
s are very strong radio sources. The directional resolution of any telescope is in principle limited by diffraction; for radio telescopes this is also the practical limit. An important improvement in obtaining positional high accuracies (from milli-arcsecond to micro-arcsecond) was obtained by combining radio telescopes across Earth. The technique is called
very long baseline interferometry Very-long-baseline interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telescopes on Earth or in space. T ...
(VLBI). With this technique radio observations couple the phase information of the radio signal observed in telescopes separated over large distances. Recently, these telescopes have measured the deflection of radio waves by the Sun to extremely high precision, confirming the amount of deflection predicted by general relativity aspect to the 0.03% level. At this level of precision systematic effects have to be carefully taken into account to determine the precise location of the telescopes on Earth. Some important effects are Earth's
nutation Nutation () is a rocking, swaying, or nodding motion in the axis of rotation of a largely axially symmetric object, such as a gyroscope, planet, or bullet in flight, or as an intended behaviour of a mechanism. In an appropriate reference frame ...
, rotation, atmospheric refraction, tectonic displacement and tidal waves. Another important effect is refraction of the radio waves by the
solar corona A corona ( coronas or coronae) is the outermost layer of a star's atmosphere. It consists of plasma. The Sun's corona lies above the chromosphere and extends millions of kilometres into outer space. It is most easily seen during a total solar e ...
. Fortunately, this effect has a characteristic
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors i ...
, whereas gravitational distortion is independent of wavelength. Thus, careful analysis, using measurements at several frequencies, can subtract this source of error. The entire sky is slightly distorted due to the gravitational deflection of light caused by the Sun (the anti-Sun direction excepted). This effect has been observed by the
European Space Agency , owners = , headquarters = Paris, Île-de-France, France , coordinates = , spaceport = Guiana Space Centre , seal = File:ESA emblem seal.png , seal_size = 130px , image = Views in the Main Control Room (1205 ...
astrometric satellite
Hipparcos ''Hipparcos'' was a scientific satellite of the European Space Agency (ESA), launched in 1989 and operated until 1993. It was the first space experiment devoted to precision astrometry, the accurate measurement of the positions of celestial obj ...
. It measured the positions of about 105 stars. During the full mission about relative positions have been determined, each to an accuracy of typically 3 milliarcseconds (the accuracy for an 8–9 magnitude star). Since the gravitation deflection perpendicular to the Earth–Sun direction is already 4.07 milliarcseconds, corrections are needed for practically all stars. Without systematic effects, the error in an individual observation of 3 milliarcseconds, could be reduced by the square root of the number of positions, leading to a precision of 0.0016 milliarcseconds. Systematic effects, however, limit the accuracy of the determination to 0.3% (Froeschlé, 1997). Launched in 2013, the ''Gaia'' spacecraft will conduct a census of one billion
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s in the
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
and measure their positions to an accuracy of 24 microarcseconds. Thus it will also provide stringent new tests of gravitational deflection of light caused by the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
which was predicted by General relativity.


Light travel time delay testing

Irwin I. Shapiro Irwin Ira Shapiro is an American astrophysicist and Timken University Professor at Harvard University. He has been a professor at Harvard since 1982. He was the director of the Center for Astrophysics Harvard & Smithsonian from 1982 to 20 ...
proposed another test, beyond the classical tests, which could be performed within the Solar System. It is sometimes called the fourth "classical" test of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
. He predicted a relativistic time delay (
Shapiro delay The Shapiro time delay effect, or gravitational time delay effect, is one of the four classic solar-system tests of general relativity. Radar signals passing near a massive object take slightly longer to travel to a target and longer to return tha ...
) in the round-trip travel time for radar signals reflecting off other planets. The mere curvature of the path of a
photon A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they always ...
passing near the Sun is too small to have an observable delaying effect (when the round-trip time is compared to the time taken if the photon had followed a straight path), but general relativity predicts a time delay that becomes progressively larger when the photon passes nearer to the Sun due to the
time dilation In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
in the
gravitational potential In classical mechanics, the gravitational potential at a location is equal to the work (energy transferred) per unit mass that would be needed to move an object to that location from a fixed reference location. It is analogous to the electric po ...
of the Sun. Observing radar reflections from Mercury and Venus just before and after they are eclipsed by the Sun agrees with general relativity theory at the 5% level. More recently, the
Cassini probe Cassini may refer to: People * Cassini (surname) * Oleg Cassini (1913-2006), American fashion designer :Cassini family: * Giovanni Domenico Cassini (1625–1712), Italian mathematician, astronomer, engineer, and astrologer * Jacques Cassini (16 ...
has undertaken a similar experiment which gave agreement with general relativity at the 0.002% level. However, the following detailed studies revealed that the measured value of the PPN parameter gamma is affected by
gravitomagnetic Gravitoelectromagnetism, abbreviated GEM, refers to a set of formal analogies between the equations for electromagnetism and relativistic gravitation; specifically: between Maxwell's field equations and an approximation, valid under certain c ...
effect caused by the orbital motion of Sun around the
barycenter In astronomy, the barycenter (or barycentre; ) is the center of mass of two or more bodies that orbit one another and is the point about which the bodies orbit. A barycenter is a dynamical point, not a physical object. It is an important conc ...
of the solar system. The gravitomagnetic effect in the Cassini radioscience experiment was implicitly postulated by B. Berotti as having a pure general relativistic origin but its theoretical value has never been tested in the experiment which effectively makes the experimental uncertainty in the measured value of gamma actually larger (by a factor of 10) than 0.002% claimed by B. Berotti and co-authors in Nature.
Very Long Baseline Interferometry Very-long-baseline interferometry (VLBI) is a type of astronomical interferometry used in radio astronomy. In VLBI a signal from an astronomical radio source, such as a quasar, is collected at multiple radio telescopes on Earth or in space. T ...
has measured velocity-dependent (gravitomagnetic) corrections to the Shapiro time delay in the field of moving Jupiter and Saturn.


The equivalence principle

The equivalence principle, in its simplest form, asserts that the trajectories of falling bodies in a gravitational field should be independent of their mass and internal structure, provided they are small enough not to disturb the environment or be affected by
tidal forces The tidal force is a gravitational effect that stretches a body along the line towards the center of mass of another body due to a gradient (difference in strength) in gravitational field from the other body; it is responsible for diverse phenomen ...
. This idea has been tested to extremely high precision by Eötvös torsion balance experiments, which look for a differential acceleration between two test masses. Constraints on this, and on the existence of a composition-dependent fifth force or gravitational
Yukawa interaction In particle physics, Yukawa's interaction or Yukawa coupling, named after Hideki Yukawa, is an interaction between particles according to the Yukawa potential. Specifically, it is a scalar field (or pseudoscalar field) and a Dirac field of the ...
are very strong, and are discussed under
fifth force In physics, there are four observed fundamental interactions (also known as fundamental forces) that form the basis of all known interactions in nature: gravitational, electromagnetic, strong nuclear, and weak nuclear forces. Some speculative the ...
and
weak equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
. A version of the equivalence principle, called the
strong equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
, asserts that self-gravitation falling bodies, such as stars, planets or black holes (which are all held together by their gravitational attraction) should follow the same trajectories in a gravitational field, provided the same conditions are satisfied. This is called the
Nordtvedt effect In theoretical astrophysics, the Nordtvedt effect refers to the relative motion between the Earth and the Moon that would be observed if the gravitational self-energy of a body contributed differently to its gravitational mass than to its inerti ...
and is most precisely tested by the Lunar Laser Ranging Experiment. Since 1969, it has continuously measured the distance from several rangefinding stations on Earth to reflectors on the Moon to approximately centimeter accuracy. These have provided a strong constraint on several of the other post-Newtonian parameters. Another part of the strong equivalence principle is the requirement that Newton's gravitational constant be constant in time, and have the same value everywhere in the universe. There are many independent observations limiting the possible variation of Newton's
gravitational constant The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in ...
, but one of the best comes from lunar rangefinding which suggests that the gravitational constant does not change by more than one part in 1011 per year. The constancy of the other constants is discussed in the
Einstein equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
section of the equivalence principle article.


Gravitational redshift and time dilation

The first of the classical tests discussed above, the
gravitational redshift In physics and general relativity, gravitational redshift (known as Einstein shift in older literature) is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy ...
, is a simple consequence of the
Einstein equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
and was predicted by Einstein in 1907. As such, it is not a test of general relativity in the same way as the post-Newtonian tests, because any theory of gravity obeying the equivalence principle should also incorporate the gravitational redshift. Nonetheless, confirming the existence of the effect was an important substantiation of relativistic gravity, since the absence of gravitational redshift would have strongly contradicted relativity. The first observation of the gravitational redshift was the measurement of the shift in the spectral lines from the
white dwarf A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes fro ...
star
Sirius Sirius is the list of brightest stars, brightest star in the night sky. Its name is derived from the Ancient Greek language, Greek word , or , meaning 'glowing' or 'scorching'. The star is designated α Canis Majoris, Latinisation ...
B by Adams in 1925, discussed above, and follow-on measurements of other white dwarfs. Because of the difficulty of the astrophysical measurement, however, experimental verification using a known terrestrial source was preferable. Experimental verification of gravitational redshift using terrestrial sources took several decades, because it is difficult to find clocks (to measure
time dilation In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
) or sources of electromagnetic radiation (to measure redshift) with a frequency that is known well enough that the effect can be accurately measured. It was confirmed experimentally for the first time in 1959 using measurements of the change in wavelength of gamma-ray photons generated with the
Mössbauer effect The Mössbauer effect, or recoilless nuclear resonance fluorescence, is a physical phenomenon discovered by Rudolf Mössbauer in 1958. It involves the resonant and recoil-free emission and absorption of gamma radiation by atomic nuclei bound in ...
, which generates radiation with a very narrow line width. The
Pound–Rebka experiment The Pound–Rebka experiment was an experiment in which gamma rays were emitted from the top of a tower and measured by a receiver at the bottom of the tower. The purpose of the experiment was to test Albert Einstein's theory of general relativit ...
measured the relative redshift of two sources situated at the top and bottom of Harvard University's Jefferson tower. The result was in excellent agreement with general relativity. This was one of the first precision experiments testing general relativity. The experiment was later improved to better than the 1% level by Pound and Snider. The blueshift of a falling photon can be found by assuming it has an equivalent mass based on its frequency E=hf (where ''h'' is Planck's constant) along with E=mc^2, a result of special relativity. Such simple derivations ignore the fact that in general relativity the experiment compares clock rates, rather than energies. In other words, the "higher energy" of the photon after it falls can be equivalently ascribed to the slower running of clocks deeper in the gravitational potential well. To fully validate general relativity, it is important to also show that the rate of arrival of the photons is greater than the rate at which they are emitted. A very accurate gravitational redshift experiment, which deals with this issue, was performed in 1976, where a
hydrogen Hydrogen is the chemical element with the symbol H and atomic number 1. Hydrogen is the lightest element. At standard conditions hydrogen is a gas of diatomic molecules having the formula . It is colorless, odorless, tasteless, non-toxic, an ...
maser A maser (, an acronym for microwave amplification by stimulated emission of radiation) is a device that produces coherent electromagnetic waves through amplification by stimulated emission. The first maser was built by Charles H. Townes, Ja ...
clock on a rocket was launched to a height of 10,000 km, and its rate compared with an identical clock on the ground. It tested the gravitational redshift to 0.007%. Although the
Global Positioning System The Global Positioning System (GPS), originally Navstar GPS, is a satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of the global navigation satellite sy ...
(GPS) is not designed as a test of fundamental physics, it must account for the gravitational redshift in its timing system, and physicists have analyzed timing data from the GPS to confirm other tests. When the first satellite was launched, some engineers resisted the prediction that a noticeable gravitational time dilation would occur, so the first satellite was launched without the clock adjustment that was later built into subsequent satellites. It showed the predicted shift of 38 microseconds per day. This rate of discrepancy is sufficient to substantially impair function of GPS within hours if not accounted for. An excellent account of the role played by general relativity in the design of GPS can be found in Ashby 2003. Other precision tests of general relativity, not discussed here, are the
Gravity Probe A Gravity Probe A (GP-A) was a space-based experiment to test the equivalence principle, a feature of Einstein's theory of relativity. It was performed jointly by the Smithsonian Astrophysical Observatory and the National Aeronautics and Space ...
satellite, launched in 1976, which showed gravity and velocity affect the ability to synchronize the rates of clocks orbiting a central mass and the
Hafele–Keating experiment The Hafele–Keating experiment was a test of the theory of relativity. In 1971, Joseph C. Hafele, a physicist, and Richard E. Keating, an astronomer, took four cesium-beam atomic clocks aboard commercial airliners. They flew twice around the ...
, which used atomic clocks in circumnavigating aircraft to test general relativity and special relativity together.


Frame-dragging tests

Tests of the
Lense–Thirring precession In general relativity, Lense–Thirring precession or the Lense–Thirring effect (; named after Josef Lense and Hans Thirring) is a Theory of relativity, relativistic correction to the precession of a gyroscope near a large rotating mass such as ...
, consisting of small secular
precession Precession is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In othe ...
s of the orbit of a test particle in motion around a central rotating mass, for example, a planet or a star, have been performed with the
LAGEOS LAGEOS, Laser Geodynamics Satellite or Laser Geometric Environmental Observation Survey, are a series of two scientific research satellites designed to provide an orbiting laser ranging benchmark for geodynamical studies of the Earth. Each satel ...
satellites, but many aspects of them remain controversial. The same effect may have been detected in the data of the
Mars Global Surveyor ''Mars Global Surveyor'' (MGS) was an American robotic space probe developed by NASA's Jet Propulsion Laboratory and launched November 1996. MGS was a global mapping mission that examined the entire planet, from the ionosphere down through the a ...
(MGS) spacecraft, a former probe in orbit around
Mars Mars is the fourth planet from the Sun and the second-smallest planet in the Solar System, only being larger than Mercury (planet), Mercury. In the English language, Mars is named for the Mars (mythology), Roman god of war. Mars is a terr ...
; also such a test raised a debate. First attempts to detect the
Sun The Sun is the star at the center of the Solar System. It is a nearly perfect ball of hot plasma, heated to incandescence by nuclear fusion reactions in its core. The Sun radiates this energy mainly as light, ultraviolet, and infrared radi ...
's Lense–Thirring effect on the perihelia of the inner
planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a you ...
s have been recently reported as well. Frame dragging would cause the orbital plane of stars orbiting near a
supermassive black hole A supermassive black hole (SMBH or sometimes SBH) is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions of times the mass of the Sun (). Black holes are a class of astronomical obj ...
to precess about the black hole spin axis. This effect should be detectable within the next few years via
astrometric Astrometry is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way. Histor ...
monitoring of stars at the center of the
Milky Way The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye ...
galaxy. By comparing the rate of orbital precession of two stars on different orbits, it is possible in principle to test the
no-hair theorem The no-hair theorem states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent ''externally'' observable ...
s of general relativity. The
Gravity Probe B Gravity Probe B (GP-B) was a satellite-based experiment to test two unverified predictions of general relativity: the geodetic effect and frame-dragging. This was to be accomplished by measuring, very precisely, tiny changes in the direction of ...
satellite, launched in 2004 and operated until 2005, detected frame-dragging and the
geodetic effect The geodetic effect (also known as geodetic precession, de Sitter precession or de Sitter effect) represents the effect of the curvature of spacetime, predicted by general relativity, on a vector carried along with an orbiting body. For example, ...
. The experiment used four quartz spheres the size of ping pong balls coated with a superconductor. Data analysis continued through 2011 due to high noise levels and difficulties in modelling the noise accurately so that a useful signal could be found. Principal investigators at
Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is consider ...
reported on May 4, 2011, that they had accurately measured the frame dragging effect relative to the distant star
IM Pegasi IM Pegasi is a variable binary star system approximately 329 light-years away in the constellation of Pegasus. With an apparent magnitude of 5.7, it is visible to the naked eye. Increased public awareness of it is due to its use as th ...
, and the calculations proved to be in line with the prediction of Einstein's theory. The results, published in ''
Physical Review Letters ''Physical Review Letters'' (''PRL''), established in 1958, is a peer-reviewed, scientific journal that is published 52 times per year by the American Physical Society. As also confirmed by various measurement standards, which include the ''Journa ...
'' measured the
geodetic effect The geodetic effect (also known as geodetic precession, de Sitter precession or de Sitter effect) represents the effect of the curvature of spacetime, predicted by general relativity, on a vector carried along with an orbiting body. For example, ...
with an error of about 0.2 percent. The results reported the frame dragging effect (caused by Earth's rotation) added up to 37 milliarcseconds with an error of about 19 percent. Investigator Francis Everitt explained that a milliarcsecond "is the width of a human hair seen at the distance of 10 miles". In January 2012,
LARES Lares ( , ; archaic , singular ''Lar'') were guardian deities in ancient Roman religion. Their origin is uncertain; they may have been hero-ancestors, guardians of the hearth, fields, boundaries, or fruitfulness, or an amalgam of these. Lares ...
satellite was launched on a
Vega Vega is the brightest star in the northern constellation of Lyra. It has the Bayer designation α Lyrae, which is Latinised to Alpha Lyrae and abbreviated Alpha Lyr or α Lyr. This star is relatively close at only from the Sun, an ...
rocket to measure Lense–Thirring effect with an accuracy of about 1%, according to its proponents. This evaluation of the actual accuracy obtainable is a subject of debate.


Tests of the gravitational potential at small distances

It is possible to test whether the gravitational potential continues with the inverse square law at very small distances. Tests so far have focused on a divergence from GR in the form of a
Yukawa potential In particle, atomic and condensed matter physics, a Yukawa potential (also called a screened Coulomb potential) is a potential named after the Japanese physicist Hideki Yukawa. The potential is of the form: :V_\text(r)= -g^2\frac, where is a m ...
V(r) = V_0\left(1 + \alpha e^\right), but no evidence for a potential of this kind has been found. The Yukawa potential with \alpha=1 has been ruled out down to \lambda = 5.6 \times 10^m.


Mössbauer rotor experiment

It was conceived as a means to measure the
time dilation In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
effect on Earth after being motivated by Einstein's
equivalence principle In the theory of general relativity, the equivalence principle is the equivalence of gravitational and inertial mass, and Albert Einstein's observation that the gravitational "force" as experienced locally while standing on a massive body (suc ...
that implies a rotating observer will be subject to the same transformations as an observer in a gravitational field. Mössbauer rotor experiments hence permit a precise terrestrial test of the
relativistic Doppler effect The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special rel ...
. From a radioactive source fixed at the center of a spinning disc or rod,
gamma rays A gamma ray, also known as gamma radiation (symbol γ or \gamma), is a penetrating form of electromagnetic radiation arising from the radioactive decay of atomic nuclei. It consists of the shortest wavelength electromagnetic waves, typically ...
travel to an absorber at the rim (in some variations of the experiment this scheme was reversed) and an unabsorbed number of them pass through depending on the rotational speed to arrive at a stationary counter (''i.e.'', detector of gamma quanta resting in the lab frame). In lieu with the
Clock hypothesis In physics and relativity, time dilation is the difference in the elapsed time as measured by two clocks. It is either due to a relative velocity between them ( special relativistic "kinetic" time dilation) or to a difference in gravitational ...
, Einstein's
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
predicts that the moving absorber's clock at the rim should retard by a specific amount due to time dilation on account of centrifugal binding alone compared to a rest frame absorber. So the transmission of gamma photons through the absorber should increase during rotation, which can be subsequently measured by the stationary counter beyond the absorber. This prediction was actually observed using the
Mössbauer effect The Mössbauer effect, or recoilless nuclear resonance fluorescence, is a physical phenomenon discovered by Rudolf Mössbauer in 1958. It involves the resonant and recoil-free emission and absorption of gamma radiation by atomic nuclei bound in ...
, since the equivalence principle, as originally suggested by Einstein, implicitly allows the association of the time dilation due to rotation (calculated as a result of the change in the detector's count rate) with gravitational time dilation. Such experiments were pioneered by Hay ''et al.'' (1960), Champeney ''et al.'' (1965), and Kündig (1963), and all of them had declared confirmation of the prediction of Einstein's theory of relativity. Be that as it may, an early 21st Century re-examination of these endeavors called into question the validity of the past obtained results claiming to have verified time dilation as predicted by Einstein's relativity theory, whereby novel experimentations were carried out that uncovered an ''extra energy shift'' between emitted and absorbed radiation next to the classical relativistic dilation of time. This discovery was first explained as discrediting
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
and successfully confirming at the laboratory scale the predictions of an alternative theory of gravity developed by T. Yarman and his colleagues. Against this development, a contentious attempt was made to explain the disclosed extra energy shift as arising from a so-far unknown and allegedly missed ''clock synchronization effect'', which was unusually awarded a prize in 2018 by the
Gravity Research Foundation The Gravity Research Foundation is an organization established in 1948 by businessman Roger Babson (founder of Babson College) to find ways to implement gravitational shielding. Over time, the foundation turned away from trying to block gravity ...
for having secured ''a new proof of general relativity''. However, at the same time period, it was revealed that said author committed several mathematical errors in his calculations, and the supposed contribution of the so-called clock synchronization to the measured time dilation is in fact practically null. As a consequence, a general relativistic explanation for the outcomes of Mössbauer rotor experiments remains open.


Strong field tests

The very strong gravitational fields that are present close to
black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
s, especially those
supermassive black hole A supermassive black hole (SMBH or sometimes SBH) is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions of times the mass of the Sun (). Black holes are a class of astronomical obj ...
s which are thought to power
active galactic nuclei An active galactic nucleus (AGN) is a compact region at the center of a galaxy that has a much-higher-than-normal luminosity over at least some portion of the electromagnetic spectrum with characteristics indicating that the luminosity is not prod ...
and the more active
quasar A quasar is an extremely Luminosity, luminous active galactic nucleus (AGN). It is pronounced , and sometimes known as a quasi-stellar object, abbreviated QSO. This emission from a galaxy nucleus is powered by a supermassive black hole with a m ...
s, belong to a field of intense active research. Observations of these quasars and active galactic nuclei are difficult, and interpretation of the observations is heavily dependent upon astrophysical models other than general relativity or competing fundamental theories of gravitation, but they are qualitatively consistent with the black hole concept as modeled in general relativity.


Binary pulsars

Pulsars A pulsar (from ''pulsating radio source'') is a highly magnetized rotating neutron star that emits beams of electromagnetic radiation out of its magnetic poles. This radiation can be observed only when a beam of emission is pointing toward Ea ...
are rapidly rotating
neutron star A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. white ...
s which emit regular radio pulses as they rotate. As such they act as clocks which allow very precise monitoring of their orbital motions. Observations of pulsars in orbit around other stars have all demonstrated substantial
periapsis An apsis (; ) is the farthest or nearest point in the orbit of a planetary body about its primary (astronomy), primary body. For example, the apsides of the Earth are called the aphelion and perihelion. General description There are two ...
precessions that cannot be accounted for classically but can be accounted for by using general relativity. For example, the Hulse–Taylor
binary pulsar A binary pulsar is a pulsar with a binary companion, often a white dwarf or neutron star. (In at least one case, the double pulsar PSR J0737-3039, the companion neutron star is another pulsar as well.) Binary pulsars are one of the few objects ...
PSR B1913+16 PSR may refer to: Organizations * Pacific School of Religion, Berkeley, California, US * Palestinian Center for Policy and Survey Research * Physicians for Social Responsibility, US ;Political parties: * Revolutionary Socialist Party (Portugal) ( ...
(a pair of neutron stars in which one is detected as a pulsar) has an observed precession of over 4° of arc per year (periastron shift per orbit only about 10−6). This precession has been used to compute the masses of the components. Similarly to the way in which atoms and molecules emit electromagnetic radiation, a gravitating mass that is in
quadrupole A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure refl ...
type or higher order vibration, or is asymmetric and in rotation, can emit gravitational waves. These
gravitational waves Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that Wave propagation, propagate as waves outward from their source at the speed of light. They were first proposed by Oliv ...
are predicted to travel at the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit ...
. For example, planets orbiting the Sun constantly lose energy via gravitational radiation, but this effect is so small that it is unlikely it will be observed in the near future (Earth radiates about 200 watts of
gravitational radiation Gravitational waves are waves of the intensity of gravity generated by the accelerated masses of an orbital binary system that propagate as waves outward from their source at the speed of light. They were first proposed by Oliver Heaviside in 1 ...
). The radiation of gravitational waves has been inferred from the
Hulse–Taylor binary The Hulse–Taylor binary is a binary star system composed of a neutron star and a pulsar (known as PSR B1913+16, PSR J1915+1606 or PSR 1913+16) which orbit around their common center of mass. It is the first binary pulsar ever discovere ...
(and other binary pulsars). Precise timing of the pulses shows that the stars orbit only approximately according to
Kepler's Laws In astronomy, Kepler's laws of planetary motion, published by Johannes Kepler between 1609 and 1619, describe the orbits of planets around the Sun. The laws modified the heliocentric theory of Nicolaus Copernicus, replacing its circular orbits ...
: over time they gradually spiral towards each other, demonstrating an
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
loss in close agreement with the predicted energy radiated by gravitational waves. For their discovery of the first binary pulsar and measuring its orbital decay due to gravitational-wave emission, Hulse and
Taylor Taylor, Taylors or Taylor's may refer to: People * Taylor (surname) ** List of people with surname Taylor * Taylor (given name), including Tayla and Taylah * Taylor sept, a branch of Scottish clan Cameron * Justice Taylor (disambiguation) Pl ...
won the 1993
Nobel Prize in Physics ) , image = Nobel Prize.png , alt = A golden medallion with an embossed image of a bearded man facing left in profile. To the left of the man is the text "ALFR•" then "NOBEL", and on the right, the text (smaller) "NAT•" then " ...
. A "double pulsar" discovered in 2003,
PSR J0737-3039 PSR may refer to: Organizations * Pacific School of Religion, Berkeley, California, US * Palestinian Center for Policy and Survey Research * Physicians for Social Responsibility, US ;Political parties: * Revolutionary Socialist Party (Portugal) ( ...
, has a periastron precession of 16.90° per year; unlike the Hulse–Taylor binary, both
neutron star A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. white ...
s are detected as pulsars, allowing precision timing of both members of the system. Due to this, the tight orbit, the fact that the system is almost edge-on, and the very low transverse velocity of the system as seen from Earth, J0737−3039 provides by far the best system for strong-field tests of general relativity known so far. Several distinct relativistic effects are observed, including orbital decay as in the Hulse–Taylor system. After observing the system for two and a half years, four independent tests of general relativity were possible, the most precise (the Shapiro delay) confirming the general relativity prediction within 0.05% (nevertheless the periastron shift per orbit is only about 0.0013% of a circle and thus it is not a higher-order relativity test). In 2013, an international team of astronomers reported new data from observing a pulsar-white dwarf system PSR J0348+0432, in which they have been able to measure a change in the orbital period of 8 millionths of a second per year, and confirmed GR predictions in a regime of extreme gravitational fields never probed before; but there are still some competing theories that would agree with these data.


Direct detection of gravitational waves

A number of
gravitational-wave detector A gravitational-wave detector (used in a gravitational-wave observatory) is any device designed to measure tiny distortions of spacetime called gravitational waves. Since the 1960s, various kinds of gravitational-wave detectors have been built ...
s have been built with the intent of directly detecting the gravitational waves emanating from such astronomical events as the merger of two
neutron star A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. white ...
s or
black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
s. In February 2016, the
Advanced LIGO The Laser Interferometer Gravitational-Wave Observatory (LIGO) is a large-scale physics experiment and observatory designed to detect cosmic gravitational waves and to develop gravitational-wave observations as an astronomical tool. Two large ...
team announced that they had directly detected gravitational waves from a stellar
binary black hole A binary black hole (BBH) is a system consisting of two black holes in close orbit around each other. Like black holes themselves, binary black holes are often divided into stellar binary black holes, formed either as remnants of high-mass binary ...
merger, with additional detections announced in June 2016, June 2017, and August 2017. General relativity predicts gravitational waves, as does any theory of gravitation in which changes in the gravitational field propagate at a finite speed. Then, the LIGO response function could discriminate among the various theories. Since gravitational waves can be directly detected, it is possible to use them to learn about the Universe. This is
gravitational-wave astronomy Gravitational-wave astronomy is an emerging branch of observational astronomy which aims to use gravitational waves (minute distortions of spacetime predicted by Albert Einstein's theory of general relativity) to collect observational data about ...
. Gravitational-wave astronomy can test general relativity by verifying that the observed waves are of the form predicted (for example, that they only have two transverse polarizations), and by checking that
black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
s are the objects described by solutions of the
Einstein field equations In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Einstein in 1915 in the form ...
. Gravitational-wave astronomy can also test Maxwell-Einstein field equations. This version of the field equations predicts that spinning magnetars (i.e., neutron stars with extremely strong magnetic dipole field) should emit gravitational waves. "These amazing observations are the confirmation of a lot of theoretical work, including Einstein's general theory of relativity, which predicts gravitational waves," said Stephen Hawking.


Direct observation of black holes

The galaxy M87 was the subject of observation by the
Event Horizon Telescope The Event Horizon Telescope (EHT) is a large telescope array consisting of a global network of radio telescopes. The EHT project combines data from several very-long-baseline interferometry (VLBI) stations around Earth, which form a combined arr ...
(EHT) in 2017; the 10 April 2019 issue of ''
Astrophysical Journal Letters ''The Astrophysical Journal'', often abbreviated ''ApJ'' (pronounced "ap jay") in references and speech, is a Peer review, peer-reviewed scientific journal of astrophysics and astronomy, established in 1895 by American astronomers George Ellery H ...
'' (vol. 875, No. 1) was dedicated to the EHT results, publishing six
open-access Open access (OA) is a set of principles and a range of practices through which research outputs are distributed online, free of access charges or other barriers. With open access strictly defined (according to the 2001 definition), or libre op ...
papers. The
event horizon In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s. In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact obj ...
of the black hole at the center of M87 was directly imaged at the wavelength of radio waves by the EHT; the image was revealed in a press conference on 10 April 2019, the first image of a black hole's event horizon. In May 2022, the EHT provided the first image of the super massive black hole Sagittarius A* in the center of our own Milky Way galaxy.


Gravitational redshift and orbit precession of star in strong gravity field

Gravitational redshift in light from the S2 star orbiting the supermassive black hole
Sagittarius A* Sagittarius A* ( ), abbreviated Sgr A* ( ), is the supermassive black hole at the Galactic Center of the Milky Way. It is located near the border of the constellations Sagittarius and Scorpius, about 5.6° south of the ecliptic, vi ...
in the center of the Milky Way has been measured with the
Very Large Telescope The Very Large Telescope (VLT) is a telescope facility operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. It consists of four individual telescopes, each with a primary mirror 8.2 m across, ...
using GRAVITY, NACO and SIFONI instruments. Additionally, there has now been detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole.


Strong equivalence principle

The strong equivalence principle of general relativity requires universality of free fall to apply even to bodies with strong self-gravity. Direct tests of this principle using Solar System bodies are limited by the weak self-gravity of the bodies, and tests using pulsar–white-dwarf binaries have been limited by the weak gravitational pull of the Milky Way. With the discovery of a triple star system called PSR J0337+1715, located about 4,200 light-years from Earth, the strong equivalence principle can be tested with a high accuracy. This system contains a
neutron star A neutron star is the collapsed core of a massive supergiant star, which had a total mass of between 10 and 25 solar masses, possibly more if the star was especially metal-rich. Except for black holes and some hypothetical objects (e.g. white ...
in a 1.6-day orbit with a
white dwarf A white dwarf is a stellar core remnant composed mostly of electron-degenerate matter. A white dwarf is very dense: its mass is comparable to the Sun's, while its volume is comparable to the Earth's. A white dwarf's faint luminosity comes fro ...
star, and the pair in a 327-day orbit with another white dwarf further away. This system permits a test that compares how the gravitational pull of the outer white dwarf affects the pulsar, which has strong self-gravity, and the inner white dwarf. The result shows that the accelerations of the pulsar and its nearby white-dwarf companion differ fractionally by no more than 2.6 (95%
confidence level In frequentist statistics, a confidence interval (CI) is a range of estimates for an unknown parameter. A confidence interval is computed at a designated ''confidence level''; the 95% confidence level is most common, but other levels, such as 9 ...
).


X-ray spectroscopy

This technique is based on the idea that photon trajectories are modified in the presence of a gravitational body. A very common astrophysical system in the universe is a
black hole A black hole is a region of spacetime where gravitation, gravity is so strong that nothing, including light or other Electromagnetic radiation, electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts t ...
surrounded by an accretion disk. The radiation from the general neighborhood, including the accretion disk, is affected by the nature of the central black hole. Assuming Einstein's theory is correct, astrophysical black holes are described by the Kerr metric. (A consequence of the
no-hair theorem The no-hair theorem states that all stationary black hole solutions of the Einstein–Maxwell equations of gravitation and electromagnetism in general relativity can be completely characterized by only three independent ''externally'' observable ...
s.) Thus, by analyzing the radiation from such systems, it is possible to test Einstein's theory. Most of the radiation from these black hole – accretion disk systems (e.g., black hole binaries and
active galactic nuclei An active galactic nucleus (AGN) is a compact region at the center of a galaxy that has a much-higher-than-normal luminosity over at least some portion of the electromagnetic spectrum with characteristics indicating that the luminosity is not prod ...
) arrives in the form of X-rays. When modeled, the radiation is decomposed into several components. Tests of Einstein's theory are possible with the thermal spectrum (only for black hole binaries) and the reflection spectrum (for both black hole binaries and active galactic nuclei). The former is not expected to provide strong constraints, while the latter is much more promising. In both cases, systematic uncertainties might make such tests more challenging.


Cosmological tests

Tests of general relativity on the largest scales are not nearly so stringent as Solar System tests. The earliest such test was the prediction and discovery of the
expansion of the universe The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not exp ...
. In 1922,
Alexander Friedmann Alexander Alexandrovich Friedmann (also spelled Friedman or Fridman ; russian: Алекса́ндр Алекса́ндрович Фри́дман) (June 16 .S. 4 1888 – September 16, 1925) was a Russian and Soviet physicist and mathematician ...
found that the Einstein equations have non-stationary solutions (even in the presence of the
cosmological constant In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equ ...
). In 1927,
Georges Lemaître Georges Henri Joseph Édouard Lemaître ( ; ; 17 July 1894 – 20 June 1966) was a Belgian Catholic priest, theoretical physicist, mathematician, astronomer, and professor of physics at the Catholic University of Louvain. He was the first to th ...
showed that static solutions of the Einstein equations, which are possible in the presence of the cosmological constant, are unstable, and therefore the static universe envisioned by Einstein could not exist (it must either expand or contract). W.Pauli, 1958, pp. 219–220 Lemaître made an explicit prediction that the universe should expand. Kragh, 2003, p. 153 He also derived a redshift-distance relationship, which is now known as the
Hubble Law Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
. Later, in 1931, Einstein himself agreed with the results of Friedmann and Lemaître. The expansion of the universe discovered by
Edwin Hubble Edwin Powell Hubble (November 20, 1889 – September 28, 1953) was an Americans, American astronomer. He played a crucial role in establishing the fields of extragalactic astronomy and observational cosmology. Hubble proved that many objects ...
in 1929 was then considered by many (and continues to be considered by some now) as a direct confirmation of general relativity. In the 1930s, largely due to the work of E. A. Milne, it was realised that the linear relationship between redshift and distance derives from the general assumption of uniformity and isotropy rather than specifically from general relativity. Rudnicki, 1991, p. 28. ''The Hubble Law was viewed by many as an observational confirmation of General Relativity in the early years'' However the prediction of a non-static universe was non-trivial, indeed dramatic, and primarily motivated by general relativity. Some other cosmological tests include searches for primordial gravitational waves generated during
cosmic inflation In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from  seconds after the conjectured Big Bang singularity ...
, which may be detected in the
cosmic microwave background In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all spac ...
polarization or by a proposed space-based
gravitational-wave interferometer A gravitational-wave detector (used in a gravitational-wave observatory) is any device designed to measure tiny distortions of spacetime called gravitational waves. Since the 1960s, various kinds of gravitational-wave detectors have been built ...
called the
Big Bang Observer The Big Bang Observer (BBO) is a proposed successor to the Laser Interferometer Space Antenna (LISA) by the European Space Agency. The primary scientific goal is the observation of gravitational waves from the time shortly after the Big Bang, b ...
. Other tests at high redshift are constraints on other theories of gravity, and the variation of the gravitational constant since
Big Bang nucleosynthesis In physical cosmology, Big Bang nucleosynthesis (abbreviated BBN, also known as primordial nucleosynthesis) is the production of nuclei other than those of the lightest isotope of hydrogen (hydrogen-1, 1H, having a single proton as a nucleus) du ...
(it varied by no more than 40% since then). In August 2017, the findings of tests conducted by astronomers using the
European Southern Observatory The European Organisation for Astronomical Research in the Southern Hemisphere, commonly referred to as the European Southern Observatory (ESO), is an intergovernmental organization, intergovernmental research organisation made up of 16 mem ...
's
Very Large Telescope The Very Large Telescope (VLT) is a telescope facility operated by the European Southern Observatory on Cerro Paranal in the Atacama Desert of northern Chile. It consists of four individual telescopes, each with a primary mirror 8.2 m across, ...
(VLT), among other instruments, were released, and positively demonstrated gravitational effects predicted by Albert Einstein. One of these tests observed the orbit of the stars circling around
Sagittarius A* Sagittarius A* ( ), abbreviated Sgr A* ( ), is the supermassive black hole at the Galactic Center of the Milky Way. It is located near the border of the constellations Sagittarius and Scorpius, about 5.6° south of the ecliptic, vi ...
, a black hole about 4 million times as massive as the sun. Einstein's theory suggested that large objects bend the space around them, causing other objects to diverge from the straight lines they would otherwise follow. Although previous studies have validated Einstein's theory, this was the first time his theory had been tested on such a gigantic object. The findings were published in ''
The Astrophysical Journal ''The Astrophysical Journal'', often abbreviated ''ApJ'' (pronounced "ap jay") in references and speech, is a peer-reviewed Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work ...
''.


Gravitational lensing

Astronomers using the Hubble Space Telescope and the Very Large Telescope have made precise tests of general relativity on galactic scales. The nearby galaxy ESO 325-G004 acts as a strong gravitational lens, distorting light from a distant galaxy behind it to create an
Einstein ring An Einstein ring, also known as an Einstein–Chwolson ring or Chwolson ring (named for Orest Chwolson), is created when light from a galaxy or star passes by a massive object en route to the Earth. Due to gravitational lensing, the light is dive ...
around its centre. By comparing the mass of ESO 325-G004 (from measurements of the motions of stars inside this galaxy) with the curvature of space around it, astronomers found that gravity behaves as predicted by general relativity on these astronomical length-scales.


See also

*
General relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
*
Tests of special relativity Special relativity is a physical theory that plays a fundamental role in the description of all physical phenomena, as long as gravitation is not significant. Many experiments played (and still play) an important role in its development and justific ...


References


Notes


Other research papers

* * * * A. Einstein, "Über das Relativitätsprinzip und die aus demselben gezogene Folgerungen", ''Jahrbuch der Radioaktivitaet und Elektronik'' 4 (1907); translated "On the relativity principle and the conclusions drawn from it", in ''The collected papers of Albert Einstein. Vol. 2 : The Swiss years: writings, 1900–1909'' (Princeton University Press, Princeton, New Jersey, 1989), Anna Beck translator. Einstein proposes the gravitational redshift of light in this paper, discussed online a
The Genesis of General Relativity
* A. Einstein, "Über den Einfluß der Schwerkraft auf die Ausbreitung des Lichtes", ''Annalen der Physik'' 35 (1911); translated "On the Influence of Gravitation on the Propagation of Light" in ''The collected papers of Albert Einstein. Vol. 3 : The Swiss years: writings, 1909–1911'' (Princeton University Press, Princeton, New Jersey, 1994), Anna Beck translator, and in ''The Principle of Relativity'', (Dover, 1924), pp 99–108, W. Perrett and G. B. Jeffery translators, . The deflection of light by the sun is predicted from the principle of equivalence. Einstein's result is half the full value found using the general theory of relativity. * * M. Froeschlé, F. Mignard and F. Arenou,
Determination of the PPN parameter γ with the Hipparcos data
Hipparcos Venice '97, ESA-SP-402 (1997). * * * *


Textbooks

* S. M. Carroll,
Spacetime and Geometry: an Introduction to General Relativity
', Addison-Wesley, 2003. A graduate-level general relativity textbook. * A. S. Eddington,
Space, Time and Gravitation
', Cambridge University Press, reprint of 1920 ed. * A. Gefter, "Putting Einstein to the Test", ''Sky and Telescope'' July 2005, p. 38. A popular discussion of tests of general relativity. * H. Ohanian and R. Ruffini, ''Gravitation and Spacetime, 2nd Edition'' Norton, New York, 1994, . A general relativity textbook. * * C. M. Will, ''Theory and Experiment in Gravitational Physics'', Cambridge University Press, Cambridge (1993). A standard technical reference. * C. M. Will, ''Was Einstein Right?: Putting General Relativity to the Test'', Basic Books (1993). This is a popular account of tests of general relativity.


Living Reviews papers

* N. Ashby
"Relativity in the Global Positioning System"
''Living Reviews in Relativity'' (2003). * C. M. Will
The Confrontation between General Relativity and Experiment
''Living Reviews in Relativity'' (2014). An online, technical review, covering much of the material in ''Theory and experiment in gravitational physics.'' It is less comprehensive but more up to date. (ArXiv version here
arxiv.org/abs/1403.7377
)


External links





(for amount of observed and GR shifts). {{DEFAULTSORT:Tests Of General Relativity Mercury (planet)