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Quadrupole Formula
In general relativity, the quadrupole formula describes the rate at which gravitational waves are emitted from a system of masses based on the change of the (mass) quadrupole moment. The formula reads : \bar_(t,r) = \frac \ddot_(t-r/c), where \bar_ is the spatial part of the trace reversed perturbation of the metric, i.e. the gravitational wave. G is the gravitational constant, c the speed of light in vacuum, and I_ is the mass quadrupole moment. It is useful to express the gravitational wave strain in the transverse traceless gauge, which is given by a similar formula where I_^ is the traceless part of the mass quadrupole moment. : _^T = \int \rho(\mathbf) \left _i r_j - \frac r^2 \delta_\right d^3 r, The total energy (luminosity) carried away by gravitational waves is : \frac = \sum_ \frac \left( \frac \right)^2 The formula was first obtained by Albert Einstein in 1918. After a long history of debate on its physical correctness, observations of energy loss due to gravit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the ' is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations. Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Wave
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 1893 and then later by Henri Poincaré in 1905 as waves similar to electromagnetic waves but the gravitational equivalent. Gravitational waves were later predicted in 1916 by Albert Einstein on the basis of his general theory of relativity as ripples in spacetime. Later he refused to accept gravitational waves. Gravitational waves transport energy as gravitational radiation, a form of radiant energy similar to electromagnetic radiation. Newton's law of universal gravitation, part of classical mechanics, does not provide for their existence, since that law is predicated on the assumption that physical interactions propagate instantaneously (at infinite speed)showing one of the ways the methods of Newtonian physics are unable to explain ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrupole Moment
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 reflecting various orders of complexity. Mathematical definition The quadrupole moment tensor ''Q'' is a rank-two tensor—3×3 matrix. There are several definitions, but it is normally stated in the traceless form (i.e. Q_ + Q_ + Q_ = 0). The quadrupole moment tensor has thus nine components, but because of transposition symmetry and zero-trace property, in this form only five of these are independent. For a discrete system of \ell point charges or masses in the case of a gravitational quadrupole, each with charge q_\ell, or mass m_\ell, and position \vec_\ell = \left(r_, r_, r_\right) relative to the coordinate system origin, the components of the ''Q'' matrix are defined by: : Q_ = \sum_\ell q_\ell\left(3r_ r_ - \left\, \vec_\ell \righ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 of relativity, but he also made important contributions to the development of the theory of quantum mechanics. Relativity and quantum mechanics are the two pillars of modern physics. His mass–energy equivalence formula , which arises from relativity theory, has been dubbed "the world's most famous equation". His work is also known for its influence on the philosophy of science. He received the 1921 Nobel Prize in Physics "for his services to theoretical physics, and especially for his discovery of the law of the photoelectric effect", a pivotal step in the development of quantum theory. His intellectual achievements and originality resulted in "Einstein" becoming synonymous with "genius". In 1905, a year sometimes described as his ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 discovered. The pulsar was discovered by Russell Alan Hulse and Joseph Hooton Taylor Jr., of the University of Massachusetts Amherst in 1974. Their discovery of the system and analysis of it earned them the 1993 Nobel Prize in Physics "for the discovery of a new type of pulsar, a discovery that has opened up new possibilities for the study of gravitation." Discovery Using the Arecibo 305 m dish, Hulse and Taylor detected pulsed radio emissions and thus identified the source as a pulsar, a rapidly rotating, highly magnetized neutron star. The neutron star rotates on its axis 17 times per second; thus the pulse period is 59 milliseconds. After timing the radio pulses for some time, Hulse and Taylor noticed that there was a systematic variation in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multipole Radiation
Multipole radiation is a theoretical framework for the description of electromagnetic or gravitational radiation from time-dependent distributions of distant sources. These tools are applied to physical phenomena which occur at a variety of length scales - from gravitational waves due to galaxy collisions to gamma radiation resulting from nuclear decay. Multipole radiation is analyzed using similar multipole expansion techniques that describe fields from static sources, however there are important differences in the details of the analysis because multipole radiation fields behave quite differently from static fields. This article is primarily concerned with electromagnetic multipole radiation, although the treatment of gravitational waves is similar. Electromagnetic radiation depends on structural details of the source system of electric charge and electric current. Direct analysis can be intractable if the structure is unknown or complicated. Multipole analysis offers a way to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Birkhoff's Theorem (relativity)
In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution (i.e. the spacetime outside of a spherical, nonrotating, gravitating body) must be given by the Schwarzschild metric. The converse of the theorem is true and is called Israel's theorem. The converse is not true in Newtonian gravity. The theorem was proven in 1923 by George David Birkhoff (author of another famous '' Birkhoff theorem'', the ''pointwise ergodic theorem'' which lies at the foundation of ergodic theory). However, Nils Voje Johansen, Finn Ravndal, Stanley Deser recently pointed out that it was published two years earlier by a little-known Norwegian physicist, Jørg Tofte Jebsen.J.T. Jebsen, ''Uber die allgemeinen kugelsymmetrischen Lösungen der Einsteinschen Gravitationsgleichungen im Vakuum'', Arkiv för matematik, astronomi och fysik, 15 (18), 1 - 9 (1921).J.T. Jebsen, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PSR J0737−3039
PSR J0737−3039 is the only known double pulsar. It consists of two neutron stars emitting electromagnetic waves in the radio wavelength in a relativistic binary system. The two pulsars are known as PSR J0737−3039A and PSR J0737−3039B. It was discovered in 2003 at Australia's Parkes Observatory by an international team led by the Italian radio astronomer Marta Burgay during a high-latitude pulsar survey. Pulsars A pulsar is a neutron star which produces pulsating radio emission due to a strong magnetic field. A neutron star is the ultra-compact remnant of a massive star which exploded as a supernova. Neutron stars have a mass bigger than our sun, yet are only a few kilometers across. These extremely dense objects rotate on their axes, producing focused electromagnetic waves which sweep around the sky in a lighthouse effect at rates that can reach a few hundred pulses per second. PSR J0737−3039 is the only known system containing two pulsars – ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the ' is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations. Newton's law of universal gravitation, which describes classical gravity, can be seen as a prediction of general relativity for the almost flat spacetime geometry around stationary mass distributions. Some predictions of general relativity, however, are beyond Newton's law of universal gravitat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 objects such as neutron stars and black holes, events such as supernovae, and processes including those of the early universe shortly after the Big Bang. Gravitational waves have a solid theoretical basis, founded upon the theory of relativity. They were first predicted by Einstein in 1916; although a specific consequence of general relativity, they are a common feature of all theories of gravity that obey special relativity. However, after 1916 there was a long debate whether the waves were actually physical, or artefacts of coordinate freedom in general relativity; this was not fully resolved until the 1950s. Indirect observational evidence for their existence first came in the late 1980s, from the monitoring of the Hulse–Taylor bin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equations Of Physics
In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign . The word ''equation'' and its cognates in other languages may have subtly different meanings; for example, in French an ''équation'' is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. ''Solving'' an equation containing variables consists of determining which values of the variables make the equality true. The variables for which the equation has to be solved are also called unknowns, and the values of the unknowns that satisfy the equality are called solutions of the equation. There are two kinds of equations: identities and conditional equations. An identity is true for all values of the variables. A conditional equation is only true for particular values of the variables. An equation is written as two expressions, connected by an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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