Jürgen Ehlers (; 29 December 1929 – 20 May 2008) was a German
physicist
A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe.
Physicists generally are interested in the root or ultimate caus ...
who contributed to the understanding of
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 ...
's 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 ...
. From graduate and postgraduate work in
Pascual Jordan
Ernst Pascual Jordan (; 18 October 1902 – 31 July 1980) was a German theoretical and mathematical physicist who made significant contributions to quantum mechanics and quantum field theory. He contributed much to the mathematical form of matri ...
's relativity research group at
Hamburg University, he held various posts as a lecturer and, later, as a professor before joining the
Max Planck Institute for Astrophysics in
Munich
Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the States of Germany, German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the List of cities in Germany by popu ...
as a director. In 1995, he became the founding director of the newly created
Max Planck Institute for Gravitational Physics
The Max Planck Institute for Gravitational Physics (Albert Einstein Institute) is a Max Planck Institute whose research is aimed at investigating Einstein's theory of relativity and beyond: Mathematics, quantum gravity, astrophysical relativity, a ...
in
Potsdam
Potsdam () is the capital and, with around 183,000 inhabitants, largest city of the German state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the River Havel, a tributary of the Elbe, downstream of B ...
, Germany.
Ehlers' research focused on the foundations of general relativity as well as on the theory's applications to
astrophysics
Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...
. He formulated a suitable classification of
exact solutions
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first i ...
to
Einstein's 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 ...
and proved the
Ehlers–Geren–Sachs theorem
The Ehlers–Geren–Sachs theorem, published in 1968 by Jürgen Ehlers, P. Geren and Rainer K. Sachs, shows that if, in a given universe, all freely falling observers measure the cosmic background radiation
Cosmic background radiation is e ...
that justifies the application of simple, general-relativistic model universes to modern
cosmology
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in ...
. He created a
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
-oriented description of
gravitational lens
A gravitational lens is a distribution of matter (such as a 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 effect is known ...
ing and clarified the relationship between models formulated within the framework of general relativity and those of
Newtonian gravity
Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distan ...
. In addition, Ehlers had a keen interest in both the history and
philosophy of physics
In philosophy, philosophy of physics deals with conceptual and interpretational issues in modern physics, many of which overlap with research done by certain kinds of theoretical physicists. Philosophy of physics can be broadly divided into thr ...
and was an ardent populariser of science.
Biography
Early life
Jürgen Ehlers was born in Hamburg on 29 December 1929.
He attended public schools from 1936 to 1949, and then went on to study physics, mathematics and philosophy at
Hamburg University from 1949 to 1955. In the winter term of 1955–56, he passed the high school teacher's examination (''
Staatsexamen
The ("state examination" or "exam by state"; pl.: ''Staatsexamina'') is a German government licensing examination that future physicians, dentists, teachers, pharmacists, food chemists, psychotherapists and jurists (i.e., lawyers, judges, public ...
''), but instead of becoming a teacher undertook graduate research with
Pascual Jordan
Ernst Pascual Jordan (; 18 October 1902 – 31 July 1980) was a German theoretical and mathematical physicist who made significant contributions to quantum mechanics and quantum field theory. He contributed much to the mathematical form of matri ...
, who acted as his thesis advisor. Ehlers' doctoral work was on the construction and characterization of 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 ...
. He earned his doctorate in physics from Hamburg University in 1958.
Prior to Ehlers' arrival, the main research of Jordan's group had been dedicated to a
scalar-tensor modification of general relativity that later became known as
Jordan–Brans–Dicke theory. This theory differs from general relativity in that the
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 ...
is replaced by a variable
field
Field may refer to:
Expanses of open ground
* Field (agriculture), an area of land used for agricultural purposes
* Airfield, an aerodrome that lacks the infrastructure of an airport
* Battlefield
* Lawn, an area of mowed grass
* Meadow, a grass ...
. Ehlers was instrumental in changing the group's focus to the structure and interpretation of Einstein's original theory. Other members of the group included Wolfgang Kundt,
Rainer K. Sachs
Rainer Kurt "Ray" Sachs (born June 13, 1932) is a German-American mathematical physicist, with interests in general relativistic cosmology and astrophysics, as well as a computational radiation biologist. He is professor emeritus of Mathematics an ...
and Manfred Trümper.
The group had a close working relationship with
Otto Heckmann
Otto Hermann Leopold Heckmann (June 23, 1901 – May 13, 1983) was a German astronomer.
He directed the Hamburg Observatory from 1941 to 1962, after which he became the first director of the European Southern Observatory. He actively contrib ...
and his student
Engelbert Schücking
Engelbert Levin Schücking (May 23, 1926 – January 5, 2015), in English-language works often cited as E. L. Schucking, was a physics professor at New York University in New York City. His research interests were theoretical astrophysics, general ...
at
Hamburger Sternwarte, the city's observatory. Guests at the group's colloquium included
Wolfgang Pauli
Wolfgang Ernst Pauli (; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics fo ...
, Joshua Goldberg and
Peter Bergmann
Peter Gabriel Bergmann (24 March 1915 – 19 October 2002) was a German-American physicist best known for his work with Albert Einstein on a unified field theory encompassing all physical interactions. He also introduced primary and secondar ...
.
In 1961, as Jordan's assistant, Ehlers earned his
habilitation
Habilitation is the highest university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, usually including a ...
, qualifying him for a German professorship. He then held teaching and research positions in Germany and in the US, namely at the
University of Kiel
Kiel University, officially the Christian-Albrecht University of Kiel, (german: Christian-Albrechts-Universität zu Kiel, abbreviated CAU, known informally as Christiana Albertina) is a university in the city of Kiel, Germany. It was founded in ...
,
Syracuse University
Syracuse University (informally 'Cuse or SU) is a Private university, private research university in Syracuse, New York. Established in 1870 with roots in the Methodist Episcopal Church, the university has been nonsectarian since 1920. Locate ...
and Hamburg University. From 1964 to 1965, he was at the
Graduate Research Center of the Southwest in
Dallas
Dallas () is the List of municipalities in Texas, third largest city in Texas and the largest city in the Dallas–Fort Worth metroplex, the List of metropolitan statistical areas, fourth-largest metropolitan area in the United States at 7.5 ...
. From 1965 to 1971, he held various positions in
Alfred Schild
Alfred Schild (September 7, 1921 – May 24, 1977) was a leading Austrian American physicist, well known for his contributions to the Golden age of general relativity (1960–1975).
Biography
Schild was born in Istanbul on September 7, 1921. His ...
's group at the
University of Texas at Austin
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 ...
, starting as an
associate professor
Associate professor is an academic title with two principal meanings: in the North American system and that of the ''Commonwealth system''.
Overview
In the ''North American system'', used in the United States and many other countries, it is a ...
and, in 1967, obtaining a position as full professor. During that time, he held visiting professorships at the universities of
Würzburg
Würzburg (; Main-Franconian: ) is a city in the region of Franconia in the north of the German state of Bavaria. Würzburg is the administrative seat of the ''Regierungsbezirk'' Lower Franconia. It spans the banks of the Main River.
Würzburg is ...
and
Bonn
The federal city of Bonn ( lat, Bonna) is a city on the banks of the Rhine in the German state of North Rhine-Westphalia, with a population of over 300,000. About south-southeast of Cologne, Bonn is in the southernmost part of the Rhine-Ruhr r ...
.
Munich
In 1970, Ehlers received an offer to join the
Max Planck Institute for Physics and Astrophysics
The Max Planck Institute for Physics and Astrophysics is a former institute of the Max Planck Society in Germany. Located in Munich, it was also known as the Werner Heisenberg Institute. The institute was founded in 1958 as a successor to the Max ...
in
Munich
Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the States of Germany, German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the List of cities in Germany by popu ...
as the director of its gravitational theory department. Ehlers had been suggested by
Ludwig Biermann
Ludwig Franz Benedikt Biermann (March 13, 1907 in Hamm – January 12, 1986 in München) was a German astronomer, obtaining his Ph.D. from Göttingen University in 1932.
He made important contributions to astrophysics and plasma physics, di ...
, the institute's director at the time. When Ehlers joined the institute in 1971, he also became an adjunct professor at Munich's
Ludwig Maximilian University
The Ludwig Maximilian University of Munich (simply University of Munich or LMU; german: Ludwig-Maximilians-Universität München) is a public research university in Munich, Germany. It is Germany's sixth-oldest university in continuous operatio ...
. In March 1991, the institute split into the
Max Planck Institute for Physics
The Max Planck Institute for Physics (MPP) is a physics institute in Munich, Germany that specializes in high energy physics and astroparticle physics. It is part of the Max-Planck-Gesellschaft and is also known as the Werner Heisenberg Institu ...
and the
Max Planck Institute for Astrophysics, where Ehlers' department found a home. Over the 24 years of his tenure, his research group was home to, among others,
Gary Gibbons
Gary William Gibbons (born 1 July 1946)
is a British theoretical physicist.
Education
Gibbons was born in Coulsdon, Surrey. He was educated at Purley County Grammar School and the University of Cambridge, where in 1969 he became a researc ...
, John Stewart and Bernd Schmidt, as well as visiting scientists including
Abhay Ashtekar
Abhay Vasant Ashtekar (born 5 July 1949) is an Indian theoretical physicist. He is the Eberly Professor of Physics and the Director of the Institute for Gravitational Physics and Geometry at Pennsylvania State University. As the creator of As ...
,
Demetrios Christodoulou
Demetrios Christodoulou ( el, Δημήτριος Χριστοδούλου; born 19 October 1951) is a Greek mathematician and physicist, who first became well known for his proof, together with Sergiu Klainerman, of the nonlinear stability of the ...
and
Brandon Carter
Brandon Carter, (born 1942) is an Australian theoretical physicist, best known for his work on the properties of black holes and for being the first to name and employ the anthropic principle in its contemporary form. He is a researcher at th ...
.
One of Ehlers'
postdoctoral students in Munich was Reinhard Breuer, who later became editor-in-chief of ''Spektrum der Wissenschaft'', the German edition of the popular-science journal ''
Scientific American
''Scientific American'', informally abbreviated ''SciAm'' or sometimes ''SA'', is an American popular science magazine. Many famous scientists, including Albert Einstein and Nikola Tesla, have contributed articles to it. In print since 1845, it i ...
''.
Potsdam
When German science institutions reorganized after
German reunification
German reunification (german: link=no, Deutsche Wiedervereinigung) was the process of re-establishing Germany as a united and fully sovereign state, which took place between 2 May 1989 and 15 March 1991. The day of 3 October 1990 when the Ge ...
in 1990, Ehlers lobbied for the establishment of an institute of the Max Planck Society dedicated to research on gravitational theory. On 9 June 1994, the Society decided to open the
Max Planck Institute for Gravitational Physics
The Max Planck Institute for Gravitational Physics (Albert Einstein Institute) is a Max Planck Institute whose research is aimed at investigating Einstein's theory of relativity and beyond: Mathematics, quantum gravity, astrophysical relativity, a ...
in
Potsdam
Potsdam () is the capital and, with around 183,000 inhabitants, largest city of the German state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the River Havel, a tributary of the Elbe, downstream of B ...
. The institute started operations on 1 April 1995, with Ehlers as its founding director and as the leader of its department for the foundations and mathematics of general relativity. Ehlers then oversaw the founding of a second institute department devoted to
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 1 ...
research and headed by
Bernard F. Schutz
Bernard F. Schutz (born August 11, 1946, in Paterson, New Jersey) is an American and naturalised British physicist. He is well-known for his research in Einstein's theory of general relativity, especially for his contributions to the detection ...
. On 31 December 1998, Ehlers retired to become founding director
emeritus
''Emeritus'' (; female: ''emerita'') is an adjective used to designate a retired chair, professor, pastor, bishop, pope, director, president, prime minister, rabbi, emperor, or other person who has been "permitted to retain as an honorary title ...
.
Ehlers continued to work at the institute until his death on 20 May 2008. He left behind his wife Anita Ehlers, his four children, Martin, Kathrin, David, and Max, as well as five grandchildren.
Research
Ehlers' research was in the field of general relativity. In particular, he made contributions to
cosmology
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in ...
, the theory of
gravitational lenses and
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 ...
. His principal concern was to clarify general relativity's mathematical structure and its consequences, separating rigorous proofs from
heuristic
A heuristic (; ), or heuristic technique, is any approach to problem solving or self-discovery that employs a practical method that is not guaranteed to be optimal, perfect, or rational, but is nevertheless sufficient for reaching an immediate, ...
conjectures.
Exact solutions
For his doctoral thesis, Ehlers turned to a question that was to shape his lifetime research. He sought exact solutions of
Einstein's 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 ...
:
model universes consistent with the laws of general relativity that are simple enough to allow for an explicit description in terms of basic mathematical expressions. These exact solutions play a key role when it comes to building general-relativistic models of physical situations. However, general relativity is a fully
covariant theory – its laws are the same, independent of which
coordinate
In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space. The order of the coordinates is sign ...
s are chosen to describe a given situation. One direct consequence is that two apparently different exact solutions could correspond to the same model universe, and differ only in their coordinates. Ehlers began to look for serviceable ways of characterizing exact solutions ''
invariantly'', that is, in ways that do not depend on coordinate choice. In order to do so, he examined ways of describing the intrinsic geometric properties of the known exact solutions.
During the 1960s, following up on his doctoral thesis, Ehlers published a series of papers, all but one in collaboration with colleagues from the Hamburg group, which later became known as the "Hamburg Bible".
The first paper, written with Jordan and Kundt, is a treatise on how to characterize exact solutions to Einstein's field equations in a systematic way. The analysis presented there uses tools from
differential geometry
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multili ...
such as the
Petrov classification
In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each event in a Lorentzian manifold.
It is mos ...
of
Weyl tensor
In differential geometry, the Weyl curvature tensor, named after Hermann Weyl, is a measure of the curvature of spacetime or, more generally, a pseudo-Riemannian manifold. Like the Riemann curvature tensor, the Weyl tensor expresses the tidal f ...
s (that is, those parts of the
Riemann tensor
In the mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the most common way used to express the curvature of Riemannian manifolds. ...
describing the
curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the canonic ...
of
space-time
In physics, spacetime is a mathematical model that combines the three-dimensional space, three dimensions of space and one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visualize S ...
that are not constrained by Einstein's equations),
isometry group In mathematics, the isometry group of a metric space is the set of all bijective isometries (i.e. bijective, distance-preserving maps) from the metric space onto itself, with the function composition as group operation. Its identity element is the ...
s and
conformal transformations. This work also includes the first definition and classification of
pp-waves, a class of simple gravitational waves.
The following papers in the series were treatises on
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 ...
(one with Sachs, one with Trümper). The work with Sachs studies, among other things,
vacuum solutions with special
algebra
Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics.
Elementary a ...
ic properties, using the 2-component
spinor
In geometry and physics, spinors are elements of a complex vector space that can be associated with Euclidean space. Like geometric vectors and more general tensors, spinors transform linearly when the Euclidean space is subjected to a slight ...
formalism. It also gives a systematic exposition of the geometric properties of bundles (in mathematical terms: congruences) of light beams. Spacetime geometry can influence the propagation of light, making them converge on or diverge from each other, or deforming the bundle's cross section without changing its area. The paper formalizes these possible changes in the bundle in terms of the bundle's expansion (convergence/divergence), and twist and shear (cross-section area-conserving deformation), linking those properties to spacetime geometry. One result is the ''Ehlers-Sachs theorem'' describing the properties of the shadow produced by a narrow beam of light encountering an opaque object. The tools developed in that work would prove essential for the discovery by
Roy Kerr
Roy Patrick Kerr (; born 16 May 1934) is a New Zealand mathematician who discovered the Kerr metric, Kerr geometry, an exact solutions in general relativity, exact solution to the Einstein field equation of general relativity. His solution mo ...
of his
Kerr solution
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact solution of the Einstein field equations of gen ...
, describing a rotating
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 ...
– one of the most important exact solutions.
The last of these seminal papers addressed the general-relativistic treatment of the mechanics of continuous media. However, useful the notion of a point mass may be in classical physics; in general relativity, such an idealized mass concentration into a single point of space is not even well-defined. That is why relativistic
hydrodynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...
, that is, the study of continuous media, is an essential part of model-building in general relativity. The paper systematically describes the basic concepts and models in what the editor of the journal ''
General Relativity and Gravitation
A general officer is an officer of high rank in the armies, and in some nations' air forces, space forces, and marines or naval infantry.
In some usages the term "general officer" refers to a rank above colonel."general, adj. and n.". OED O ...
'', on the occasion of publishing an English translation 32 years after the original publication date, called "one of the best reviews in this area".
Another part of Ehlers' exploration of exact solutions in his thesis led to a result that proved important later. At the time he started his research on his doctoral thesis, the
Golden age of general relativity
General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915. According to general relativity, the observed gravitational attraction between masses results ...
had not yet begun and the basic properties and concepts of black holes were not yet understood. In the work that led to his doctoral thesis, Ehlers proved important properties of the surface around a black hole that would later be identified as its
horizon
The horizon is the apparent line that separates the surface of a celestial body from its sky when viewed from the perspective of an observer on or near the surface of the relevant body. This line divides all viewing directions based on whether i ...
, in particular that the
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 ...
inside cannot be static, but must change over time. The simplest example of this is the "Einstein-Rosen bridge", or
Schwarzschild wormhole that is part of the Schwarzschild solution describing an idealized, spherically symmetric black hole: the interior of the horizon houses a bridge-like connection that changes over time, collapsing sufficiently quickly to keep any space-traveler from traveling through the wormhole.
Ehlers group
In physics,
duality means that two equivalent descriptions of a particular physical situation exist, using different physical concepts. This is a special case of a physical
symmetry
Symmetry (from grc, συμμετρία "agreement in dimensions, due proportion, arrangement") in everyday language refers to a sense of harmonious and beautiful proportion and balance. In mathematics, "symmetry" has a more precise definit ...
, that is, a change that preserves key features of a physical system. A simple example for a duality is that between the
electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
E and the
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
B
electrodynamics
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
: In the complete absence of electrical charges, the replacement E
–B, B
E leaves
Maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
...
invariant. Whenever a particular pair of expressions for B and E conform to the laws of electrodynamics, switching the two expressions around and adding a minus sign to the new B is also valid.
In his doctoral thesis, Ehlers pointed out a duality symmetry between different components of the
metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathem ...
of a stationary
vacuum
A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often dis ...
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differen ...
, which maps solutions of Einstein's field equations to other solutions. This symmetry between the tt-component of the metric, which describes time as measured by clocks whose spatial coordinates do not change, and a term known as the ''twist potential'' is analogous to the aforementioned duality between E and B.
The duality discovered by Ehlers was later expanded to a larger symmetry corresponding to the
special linear group
In mathematics, the special linear group of degree ''n'' over a field ''F'' is the set of matrices with determinant 1, with the group operations of ordinary matrix multiplication and matrix inversion. This is the normal subgroup of the genera ...
. This larger
symmetry group
In group theory, the symmetry group of a geometric object is the group of all transformations under which the object is invariant, endowed with the group operation of composition. Such a transformation is an invertible mapping of the ambient ...
has since become known as the ''Ehlers group''. Its discovery led to further generalizations, notably the infinite-dimensional
Geroch group The Geroch group is an infinite-dimensional symmetry group of axisymmetric, :wikt:stationary, stationary vacuum spacetimes that are solutions of Einstein's equations of general relativity. It is generated by two commutativity, non-commuting subgrou ...
(the Geroch group is generated by two
non-commuting subgroup
In group theory, a branch of mathematics, given a group ''G'' under a binary operation ∗, a subset ''H'' of ''G'' is called a subgroup of ''G'' if ''H'' also forms a group under the operation ∗. More precisely, ''H'' is a subgroup ...
s, one of which is the Ehlers group). These so-called ''hidden symmetries'' play an important role in the
Kaluza–Klein reduction of both general relativity and its generalizations, such as eleven-dimensional
supergravity
In theoretical physics, supergravity (supergravity theory; SUGRA for short) is a modern field theory that combines the principles of supersymmetry and general relativity; this is in contrast to non-gravitational supersymmetric theories such as ...
. Other applications include their use as a tool in the discovery of previously unknown solutions and their role in a proof that solutions in the stationary
axi-symmetric
In geometry, circular symmetry is a type of continuous symmetry for a planar object that can be rotated by any arbitrary angle and map onto itself.
Rotational circular symmetry is isomorphic with the circle group in the complex plane, or the ...
case form an
integrable system
In mathematics, integrability is a property of certain dynamical systems. While there are several distinct formal definitions, informally speaking, an integrable system is a dynamical system with sufficiently many conserved quantities, or first ...
.
Cosmology: Ehlers–Geren–Sachs theorem
![WMAP 2010](https://upload.wikimedia.org/wikipedia/commons/2/2d/WMAP_2010.png)
The Ehlers–Geren–Sachs theorem, published in 1968, shows that in a given universe, if all freely falling observers measure the
cosmic background radiation
Cosmic background radiation is electromagnetic radiation from the Big Bang. The origin of this radiation depends on the region of the spectrum that is observed. One component is the cosmic microwave background. This component is redshifted pho ...
to have exactly the same properties in all directions (that is, they measure the background radiation to be
isotropic
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe ...
), then that universe is an isotropic and homogeneous
Friedmann–Lemaître spacetime. Cosmic isotropy and homogeneity are important as they are the basis of the modern standard model of cosmology.
Fundamental concepts in general relativity
In the 1960s, Ehlers collaborated with
Felix Pirani
__NOTOC__
Felix Arnold Edward Pirani (2 February 1928 – 31 December 2015) was a British theoretical physicist, and professor at King's College London, specialising in gravitational physics and general relativity.
Pirani and Hermann Bondi w ...
and
Alfred Schild
Alfred Schild (September 7, 1921 – May 24, 1977) was a leading Austrian American physicist, well known for his contributions to the Golden age of general relativity (1960–1975).
Biography
Schild was born in Istanbul on September 7, 1921. His ...
on a constructive-axiomatic approach to general relativity: a way of deriving the theory from a minimal set of elementary objects and a set of axioms specifying these objects' properties. The basic ingredients of their approach are primitive concepts such as
event
Event may refer to:
Gatherings of people
* Ceremony, an event of ritual significance, performed on a special occasion
* Convention (meeting), a gathering of individuals engaged in some common interest
* Event management, the organization of e ...
,
light
Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 tera ...
ray,
particle
In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object which can be described by several physical property, physical or chemical property, chemical ...
and
freely falling particle. At the outset, spacetime is a mere set of events, without any further structure. They postulated the basic properties of light and freely falling particles as axioms, and with their help constructed the
differential topology
In mathematics, differential topology is the field dealing with the topological properties and smooth properties of smooth manifolds. In this sense differential topology is distinct from the closely related field of differential geometry, which ...
,
conformal structure
In mathematics, conformal geometry is the study of the set of angle-preserving ( conformal) transformations on a space.
In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two d ...
and, finally, the
metric
Metric or metrical may refer to:
* Metric system, an internationally adopted decimal system of measurement
* An adjective indicating relation to measurement in general, or a noun describing a specific type of measurement
Mathematics
In mathem ...
structure of spacetime, that is: the notion of when two events are close to each other, the role of light rays in linking up events, and a notion of distance between events. Key steps of the construction correspond to idealized measurements, such the standard range finding used in
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 final step derived Einstein's equations from the weakest possible set of additional axioms. The result is a formulation that clearly identifies the assumptions underlying general relativity.
In the 1970s, in collaboration with Ekkart Rudolph, Ehlers addressed the problem of rigid bodies in general relativity. Rigid bodies are a fundamental concept in classical physics. However, the fact that by definition their different parts move simultaneously is incompatible with the relativistic concept of 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 ...
as a limiting speed for the propagation of signals and other influences. While, as early as 1909,
Max Born
Max Born (; 11 December 1882 – 5 January 1970) was a German physicist and mathematician who was instrumental in the development of quantum mechanics. He also made contributions to solid-state physics and optics and supervised the work of a n ...
had given a definition of rigidity that was compatible with relativistic physics, his definition depends on assumptions that are not satisfied in a general space-time, and are thus overly restrictive. Ehlers and Rudolph generalized Born's definition to a more readily applicable definition they called "pseudo-rigidity", which represents a more satisfactory approximation to the rigidity of classical physics.
Gravitational lensing
![Gravitational lens-full](https://upload.wikimedia.org/wikipedia/commons/0/02/Gravitational_lens-full.jpg)
With Peter Schneider, Ehlers embarked on an in-depth study of the foundations of
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 ...
. One result of this work was a 1992 monograph co-authored with Schneider and Emilio Falco. It was the first systematic exposition of the topic that included both the theoretical foundations and the observational results. From the viewpoint of astronomy, gravitational lensing is often described using a quasi-Newtonian approximation—assuming the
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 ...
to be small and the deflection angles to be minute—which is perfectly sufficient for most situations of astrophysical relevance. In contrast, the monograph developed a thorough and complete description of gravitational lensing from a fully relativistic space-time perspective. This feature of the book played a major part in its long-term positive reception. In the following years, Ehlers continued his research on the propagation of bundles of light in arbitrary spacetimes.
Frame theory and Newtonian gravity
A basic derivation of the Newtonian limit of general relativity is as old as the theory itself. Einstein used it to derive predictions such as the
anomalous perihelion precession of the planet
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 ...
. Later work by
Élie Cartan
Élie Joseph Cartan (; 9 April 1869 – 6 May 1951) was an influential French mathematician who did fundamental work in the theory of Lie groups, differential systems (coordinate-free geometric formulation of PDEs), and differential geometry. ...
,
Kurt Friedrichs and others showed more concretely how a geometrical generalization of
Newton's theory of gravity known as
Newton–Cartan theory Newton–Cartan theory (or geometrized Newtonian gravitation) is a geometrical re-formulation, as well as a generalization, of Newtonian gravity first introduced by Élie Cartan and Kurt Friedrichs and later developed by Dautcourt, Dixon, Dombrowsk ...
could be understood as a (degenerate) limit 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 ...
. This required letting a specific parameter
go to zero. Ehlers extended this work by developing a ''frame theory'' that allowed for constructing the Newton–Cartan limit, and in a mathematically precise way, not only for the physical laws, but for any spacetime obeying those laws (that is, solutions of Einstein's equations). This allowed physicists to explore what the Newtonian limit meant in specific physical situations. For example, the frame theory can be used to show that the Newtonian limit of a
Schwarzschild black hole is a simple
point particle
A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particles heavily used in physics. Its defining feature is that it lacks spatial extension; being dimensionless, it does not take up ...
. Also, it allows Newtonian versions of exact solutions such as the
Friedmann–Lemaître models or the
Gödel universe to be constructed. Since its inception, ideas Ehlers introduced in the context of his frame theory have found important applications in the study of both the Newtonian limit of general relativity and of the
Post-Newtonian expansion
In general relativity, the post-Newtonian expansions (PN expansions) are used for finding an approximate solution of the Einstein field equations for the metric tensor. The approximations are expanded in small parameters which express orders of ...
, where Newtonian gravity is complemented by terms of ever higher order in
in order to accommodate relativistic effects.
General relativity is
non-linear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other ...
: the gravitational influence of two masses is not simply the sum of those masses' individual gravitational influences, as had been the case in Newtonian gravity. Ehlers participated in the discussion of how the
back-reaction from gravitational radiation onto a radiating system could be systematically described in a non-linear theory such as general relativity, pointing out that the standard
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 ...
formula for the energy flux for systems like the
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 ...
had not (yet) been rigorously derived: a priori, a derivation demanded the inclusion of higher-order terms than was commonly assumed, higher than were computed until then.
His work on the Newtonian limit, particularly in relation to
cosmological
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount's ''Glossographia'', and in 1731 taken up in Latin by German philosopher ...
solutions, led Ehlers, together with his former doctoral student Thomas Buchert, to a systematic study of
perturbations and inhomogeneities in a Newtonian cosmos. This laid the groundwork for Buchert's later generalization of this treatment of inhomogeneities. This generalization was the basis of his attempt to explain what is currently seen as the cosmic effects of a
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 ...
or, in modern parlance,
dark energy
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
, as a non-linear consequence of inhomogeneities in general-relativistic cosmology.
History and philosophy of physics
Complementing his interest in the foundations of general relativity and, more generally, of physics, Ehlers researched the history of physics. Up until his death, he collaborated in a project on the history of quantum theory at the
Max Planck Institute for the History of Science
The Max Planck Institute for the History of Science (German: Max-Planck-Institut für Wissenschaftsgeschichte) is a scientific research institute founded in March 1994. It is dedicated to addressing fundamental questions of the history of knowledg ...
in Berlin. In particular, he explored Pascual Jordan's seminal contributions to the development of
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
between 1925 and 1928. Throughout his career, Ehlers had an interest in the philosophical foundations and implications of physics and contributed to research on this topic by addressing questions such as the basic status of scientific knowledge in physics.
Science popularization
Ehlers showed a keen interest in reaching a general audience. He was a frequent public lecturer, at universities as well as at venues such as the
Urania
Urania ( ; grc, , Ouranía; modern Greek shortened name ''Ránia''; meaning "heavenly" or "of heaven") was, in Greek mythology, the muse of astronomy, and in later times, of Christian poetry. Urania is the goddess of astronomy and stars, he ...
in
Berlin
Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constitue ...
. He authored popular-science articles, including contributions to general-audience journals such as ''Bild der Wissenschaft''. He edited a compilation of articles on gravity for the German edition of ''Scientific American''.
Ehlers directly addressed physics teachers, in talks and journal articles on the teaching of relativity and related basic ideas, such as
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
as the language of physics.
Honours and awards
Ehlers became a member of the
Berlin-Brandenburg Academy of Sciences and Humanities
The Berlin-Brandenburg Academy of Sciences and Humanities (german: Berlin-Brandenburgische Akademie der Wissenschaften), abbreviated BBAW, is the official academic society for the natural sciences and humanities for the States of Germany, German ...
(1993), the
Akademie der Wissenschaften und der Literatur
The Academy of Sciences and Literature (german: Akademie der Wissenschaften und der Literatur Mainz, AdW Mainz) is a scientific academy in Mainz, Germany. It was established in 1949 on an initiative of Alfred Döblin. The academy's goal is to s ...
,
Mainz
Mainz () is the capital and largest city of Rhineland-Palatinate, Germany.
Mainz is on the left bank of the Rhine, opposite to the place that the Main (river), Main joins the Rhine. Downstream of the confluence, the Rhine flows to the north-we ...
(1972), the
Leopoldina Leopoldina may refer to:
* Colônia Leopoldina, a Brazilian municipality in the state of Alagoa
* Leopoldina, Minas Gerais, a Brazilian municipality in the state of Minas Gerais
* Maria Leopoldina of Austria (1797-1826), consort of emperor Pedro I ...
in
Halle (1975) and the
Bavarian Academy of Sciences and Humanities in Munich (1979). From 1995 to 1998, he served as president of the
International Society on General Relativity and Gravitation The International Society on General Relativity and Gravitation (ISGRG) is a learned society established in 1971 with the goal to promote research on general relativity (GR) and gravitation. To that end, it encourages communication between relativi ...
. He also received the 2002
Max Planck Medal
The Max Planck medal is the highest award of the German Physical Society , the world's largest organization of physicists, for extraordinary achievements in theoretical physics. The prize has been awarded annually since 1929, with few exceptions, ...
of the
German Physical Society
The German Physical Society (German: , DPG) is the oldest organisation of physicists. The DPG's worldwide membership is cited as 60,547, as of 2019, making it the largest physics society in the world. It holds an annual conference () and multiple ...
, the
Volta Gold Medal of
Pavia University
The University of Pavia ( it, Università degli Studi di Pavia, UNIPV or ''Università di Pavia''; la, Alma Ticinensis Universitas) is a university located in Pavia, Lombardy, Italy. There was evidence of teaching as early as 1361, making it one ...
(2005) and the medal of the Faculty of Natural Sciences of
Charles University
)
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, type = Public, Ancient
, budget = 8.9 billion CZK
, rector = Milena Králíčková
, faculty = 4,057
, administrative_staff = 4,026
, students = 51,438
, undergr ...
,
Prague
Prague ( ; cs, Praha ; german: Prag, ; la, Praga) is the capital and largest city in the Czech Republic, and the historical capital of Bohemia. On the Vltava river, Prague is home to about 1.3 million people. The city has a temperate ...
(2007).
In 2008, the International Society on General Relativity and Gravitation instituted the "Jürgen Ehlers Thesis Prize" in commemoration of Ehlers. It is sponsored by the scientific publishing house
Springer
Springer or springers may refer to:
Publishers
* Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded in 1842 in Germany formerly known as Springer-Verlag.
** Springer Nature, a multinationa ...
and is awarded triennially, at the society's international conference, to the best doctoral thesis in the areas of mathematical and numerical general relativity. Issue 9 of volume 41 of the journal ''
General Relativity and Gravitation
A general officer is an officer of high rank in the armies, and in some nations' air forces, space forces, and marines or naval infantry.
In some usages the term "general officer" refers to a rank above colonel."general, adj. and n.". OED O ...
'' was dedicated to Ehlers, in memoriam.
Selected publications
*
*
*
Notes
References
*
*
* (in German, English translation of title: ''Where time and space end. The co-founder of the Max Planck Institute for Gravitational Physics, Jürgen Ehlers, has died unexpectedly'')
* (in German)
*
* (in German, English translation of title ''Jürgen Ehlers and the Theory of Relativity'')
*
*
*
*
* (dissertation, in German; title in English translation: ''Constructions and characterizations of solutions to Einstein's gravitational field equations'')
*
*
* (in German, English translation of contribution title: ''Models in physics''; English translation of title: ''Models of thinking'')
* (in German, English translation of title: ''Gaining knowledge in physics, shown for the example of the transition from Newton's spacetime to Einstein's special theory of relativity'')
* (in German, English translation of title: ''Mathematics as the "language" of physics'')
*
*
*
*
*
*.
*.
*
*
* (in German)
*
*
*
*
* (in German)
*
* (in German, English translation of title: ''Contributions to the theory of pure gravitational radiation'')
*
*
* (in German)
*
*
*
*
*
*
* (in German)
*
*
*
*
*
* (in German, English translation of title: ''Handbook of Scientific Members'').
External links
*
*
* Page
In Memoriam Jürgen Ehlersat the
Albert Einstein Institute
{{DEFAULTSORT:Ehlers, Jurgen
1929 births
2008 deaths
German cosmologists
German relativity theorists
Scientists from Hamburg
University of Hamburg alumni
Winners of the Max Planck Medal
Max Planck Institute directors