Jürgen Ehlers; (December 29, 1929–20 May 20, 2008) was a German physicist who contributed to the understanding of Albert Einstein's theory of general relativity. From graduate and postgraduate work in Pascual Jordan'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 as a director. In 1995, he became the founding director of the newly created Max Planck Institute for Gravitational Physics in Potsdam, Germany.
Ehlers' research focused on the foundations of general relativity as well as on the theory's applications to astrophysics. He formulated a suitable classification of exact solutions to Einstein's field equations and proved the Ehlers–Geren–Sachs theorem that justifies the application of simple, generalrelativistic model universes to modern cosmology. He created a spacetimeoriented description of gravitational lensing and clarified the relationship between models formulated within the framework of general relativity and those of Newtonian gravity. In addition, Ehlers had a keen interest in both the history and philosophy of physics and was an ardent populariser of science.
Early life
Jürgen Ehlers was born in Hamburg. 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), but instead of becoming a teacher undertook graduate research with Pascual Jordan, who acted as his thesis advisor. Ehlers' doctoral work was on the construction and characterization of solutions of the Einstein field equations. He earned his doctorate in physics from Hamburg University in 1958.[1]
Prior to Ehlers' arrival, the main research of Jordan's group had been dedicated to a scalartensor modification of general relativity that later became known as Jordan–Brans–Dicke theory. This theory differs from general relativity in that the gravitational constant is replaced by a variable field. Ehlers was instrumental in changing the group's focus to the structure and interpretation of Einstein's original theory.[2] Other members of the group included Wolfgang Kundt, Rainer K. Sachs and Manfred Trümper.[3] The group had a close working relationship with Otto Heckmann and his student Engelbert Schücking at Hamburger Sternwarte, the city's observatory. Guests at the group's colloquium included Wolfgang Pauli, Joshua Goldberg and Peter Bergmann.[4]
In 1961, as Jordan's assistant, Ehlers earned his habilitation, 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, Syracuse University and Hamburg University. From 1964 to 1965, he was at the Graduate Research Center of the Southwest in Dallas. From 1965 to 1971, he held various positions in Alfred Schild's group at the University of Texas at Austin, starting as an associate professor and, in 1967, obtaining a position as full professor. During that time, he held visiting professorships at the universities of Würzburg and Bonn.[5]
Munich
In 1970, Ehlers received an offer to join the Max Planck Institute for Physics and Astrophysics in Munich as the director of its gravitational theory department.[6] Ehlers had been suggested by Ludwig Biermann, 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. In March 1991, the institute split into the Max Planck Institute for Physics and the Max Planck Institute for Astrophysics, where Ehlers' department found a home.[7] Over the 24 years of his tenure, his research group was home to, among others, Gary Gibbons, John Stewart and Bernd Schmidt, as well as visiting scientists including Abhay Ashtekar, Demetrios Christodoulou and Brandon Carter.[8]
One of Ehlers' postdoctoral students in Munich was Reinhard Breuer, who later became editorinchief of Spektrum der Wissenschaft, the German edition of the popularscience journal Scientific American.[9]
Potsdam
When German science institutions reorganized after German reunification 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 in Potsdam. 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.[10] Ehlers then oversaw the founding of a second institute department devoted to gravitational wave research and headed by Bernard F. Schutz. On 31 December 1998, Ehlers retired to become founding director emeritus.[11]
Ehlers continued to work at the institute until his death on 20 May 2008.[12] He left behind his wife Anita Ehlers, his four children, Martin, Kathrin, David, and Max, as well as five grandchildren.[13]
Research
Ehlers' research was in the field of general relativity. In particular, he made contributions to cosmology, the theory of gravitational lenses and gravitational waves. His principal concern was to clarify general relativity's mathematical structure and its consequences, separating rigorous proofs from heuristic conjectures.[14]
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: 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 generalrelativistic models of physical situations. However, general relativity is a fully covariant theory – its laws are the same, independent of which coordinates 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.[15]
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".[16] 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 such as the Petrov classification of Weyl tensors (that is, those parts of the Riemann tensor describing the curvature of spacetime that are not constrained by Einstein's equations), isometry groups and conformal transformations. This work also includes the first definition and classification of ppwaves, a class of simple gravitational waves.[17]
The following papers in the series were treatises on gravitational radiation (one with Sachs, one with Trümper). The work with Sachs studies, among other things, vacuum solutions with special algebraic properties, using the 2component spinor 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 (crosssection areaconserving deformation), linking those properties to spacetime geometry. One result is the EhlersSachs 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 of his Kerr solution, describing a rotating black hole – one of the most important exact solutions.[18]
The last of these seminal papers addressed the generalrelativistic 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 welldefined. That is why relativistic hydrodynamics, that is, the study of continuous media, is an essential part of modelbuilding in general relativity. The paper systematically describes the basic concepts and models in what the editor of the journal General Relativity and Gravitation, on the occasion of publishing an English translation 32 years after the original publication date, called "one of the best reviews in this area".[19]
Another part of Ehlers' exploration of exact solutions in his thesis led to a result that proved important later. At the time Ehlers started his research on his doctoral thesis, the Golden age of general relativity 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, in particular that the gravitational field inside cannot be static, but must change over time. The simplest example of this is the "EinsteinRosen 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 bridgelike connection that changes over time, collapsing sufficiently quickly to keep any spacetraveler from traveling through the wormhole.[20]
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, that is, a change that preserves key features of a physical system. A simple example for a duality is that between the electric field E and the magnetic field B electrodynamics: In the complete absence of electrical charges, the replacement E →\to –B, B →\to E leaves Maxwell's equations 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.[21]
In his doctoral thesis, Ehlers pointed out a duality symmetry between different components of the metric of a stationary vacuum spacetime, which maps solutions of Einstein's field equations to other solutions. This symmetry between the ttcomponent 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.[22]
The duality discovered by Ehlers was later expanded to a larger symmetry corresponding to the special linear group SL(2). This larger symmetry group has since become known as the Ehlers group. Its discovery led to further generalizations, notably the infinitedimensional Geroch group (the Geroch group is generated by two noncommuting subgroups, one of which is the Ehlers group). These socalled hidden symmetries play an important role in the Kaluza–Klein reduction of both general relativity and its generalizations, such as elevendimensional supergravity. 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 axisymmetric case form an integrable system.[23]
Cosmology: Ehlers–Geren–Sachs theorem
The inhomogeneities in the temperature of the cosmic background radiation recorded in this image from the satellite probe WMAP amount to no more than 10−4 Kelvin.
The Ehlers–Geren–Sachs theorem, published in 1968, shows that in a given universe, if all freely falling observers measure the cosmic background radiation to have exactly the same properties in all directions (that is, they measure the background radiation to be isotropic), then that universe is an isotropic and homogeneous Friedmann–Lemaître spacetime.[24] Cosmic isotropy and homogeneity are important as they are the basis of the modern standard model of cosmology.[25]
Fundamental concepts in general relativity
In the 1960s, Ehlers collaborated with Felix Pirani and Alfred Schild on a constructiveaxiomatic 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, light ray, particle 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, conformal structure and, finally, the metric 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. 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.[26]
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 as a limiting speed for the propagation of signals and other influences. While, as early as 1909, Max Born had given a definition of rigidity that was compatible with relativistic physics, his definition depends on assumptions that are not satisfied in a general spacetime, and are thus overly restrictive. Ehlers and Rudolph generalized Born's definition to a more readily applicable definition they called "pseudorigidity", which represents a more satisfactory approximation to the rigidity of classical physics.[27]
Gravitational lensing
Most astrophysical modeling of gravitational lens systems makes use of the quasiNewtonian approximation
With Peter Schneider, Ehlers embarked on an indepth study of the foundations of gravitational lensing. One result of this work was a 1992 monograph coauthored 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 quasiNewtonian approximation—assuming the gravitational field 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 spacetime perspective. This feature of the book played a major part in its longterm positive reception.[28] In the following years, Ehlers continued his research on the propagation of bundles of light in arbitrary spacetimes.[29]
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. Later work by Élie Cartan, Kurt Friedrichs and others showed more concretely how a geometrical generalization of Newton's theory of gravity known as Newton–Cartan theory could be understood as a (degenerate) limit of general relativity. This required letting a specific parameter
λ\lambda 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. Also, it allows Newtonian versions of exact solutions such as the Friedmann–Lemaître models or the Gödel universe to be constructed.[30] 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 PostNewtonian expansion, where Newtonian gravity is complemented by terms of ever higher order in 1/c^{2} in order to accommodate relativistic effects.[31]
General relativity is nonlinear: 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 backreaction from gravitational radiation onto a radiating system could be systematically described in a nonlinear theory such as general relativity, pointing out that the standard quadrupole formula for the energy flux for systems like the binary pulsar had not (yet) been rigorously derived: a priori, a derivation demanded the inclusion of higherorder terms than was commonly assumed, higher than were computed until then.[32]
His work on the Newtonian limit, particularly in relation to cosmological 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 or, in modern parlance, dark energy, as a nonlinear consequence of inhomogeneities in generalrelativistic cosmology.[33]
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 in Berlin.[34] In particular, he explored Pascual Jordan's seminal contributions to the development of quantum field theory between 1925 and 1928.[35] 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.[36]
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 in Berlin. He authored popularscience articles, including contributions to generalaudience journals such as Bild der Wissenschaft. He edited a compilation of articles on gravity for the German edition of Scientific American.[37] Ehlers directly addressed physics teachers, in talks and journal articles on the teaching of relativity and related basic ideas, such as mathematics as the language of physics.[38]
Honours and awards
Ehlers became a member of the BerlinBrandenburg Academy of Sciences and Humanities (1993), the Akademie der Wissenschaften und der Literatur, Mainz (1972), the Leopoldina in Halle (1975) and the Bavarian Academy of Sciences and Humanities in Munich (1979).[39] From 1995 to 1998, he served as president of the International Society on General Relativity and Gravitation.[40] He also received the 2002 Max Planck Medal of the German Physical Society, the Volta Gold Medal of Pavia University (2005) and the medal of the Faculty of Natural Sciences of Charles University, Prague (2007).[41]
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 and is awarded triennially, at the society's international conference, to the best doctoral thesis in the areas of mathematical and numerical general relativity.[42] Issue 9 of volume 41 of the journal General Relativity and Gravitation was dedicated to Ehlers, in memoriam.[43]
Born in 1929, Ehlers studied both mathematics and physics in Hamburg in the 1950s, and he finally chose physics because he could study general relativity with Pascual Jordan, one of the pioneers of quantum physics. At this time, interest in general relativity among theoretical physicists was beginning to revive after decades of neglect. Jordan was one of a handful of senior figures around the world who felt it was time to begin to understand general relativity, in order ultimately to generalize it into a full quantum theory of gravity. Key goals were to understand gravitational waves and what we now call black holes, and Jordan and his school, including Ehlers, were among the pioneers in this revival.
After visiting positions at several universities in Germany and the United States, culminating in a professorship in 1967 at the University of Texas at Austin, Ehlers moved to Munich to become a Member of the Max Planck Institute for Physics and Astrophysics in 1971. Institute director Ludwig Biermann asked Ehlers to join the Astrophysics part of the institute, because the institute was just beginning the gravitational wave activities that would eventually lead to Germany's GEO600 detector. In 1978 Ehlers organized the Ninth Texas Symposium on Relativistic Astrophysics, the principal international meeting where relativists and astrophysicists meet and update one another on their recent research. When the Astrophysics part of the Max Planck Institute moved into a new building in Garching outside Munich in 1979, Ehlers and his group, as well as the gravitational wave experimenters, went with it. Ehlers' clear commitment to astrophysics reflected his clear belief that the most important questions in general relativity were those that would be tested by astronomical observations.
Ehlers nevertheless remained a deeply mathematical physicist, and he always insisted that the great physical and astrophysical questions about relativity theory should be answered with as much rigour and care as possible. But always the important questions for him were those that the Universe itself posed. The discovery in 1974 of the first pulsar in a binary system, by Russell Hulse and Joseph Taylor, was a watershed for relativity, because it was immediately clear that the system would provide the first clean observational test of gravitational wave theory: the two stars would gradually spiral closer to one another as gravitational waves carried energy away. Ehlers quickly grasped how important this result would be, and just as quickly pointed out that the state of the theory of gravitational radiation itself was by no means satisfactory; relativity could not properly be tested against the observations until relativists sorted out the theory.
For the next ten years, Ehlers pushed his own research associates and scientists around the world to do this, with considerable success. The award of the 1993 Nobel Prize to Hulse and Taylor, the building of giant gravitational wave detectors around the world since the 1990s, and the use of modern supercomputers to predict gravitational wave emission from neutron stars and black holes all rest on secure theoretical foundations, thanks in part to Ehlers' insistence that even the complex mathematics of general relativity should be done carefully and rigourously.
Always looking ahead for the big challenges, Ehlers in the late 1980s took up research into another of Einstein's predictions, the bending of light by gravity. Again he was motivated by recent astronomical discoveries of gravitational lensing, where telescopes see multiple images of the same object, created as light takes multiple paths to the Earth through the gravitational field of an intervening galaxy. But again the theory needed work, and Ehlers stimulated young scientists in Garching to do it better. Today gravitational lensing is a central tool in astronomy, used among other things to prove that the Universe contains far more dark matter than it does stars and visible galaxies. The nature of this dark matter is not known, but it certainly is not composed of the protons, electrons, and neutrons that dominate the world we experience. Ehlers' young associates have gone on to make important and leading contributions to this branch of astronomy.
Ehlers' work at the junction between mathematics and physics had strong influences on the development of mathematics as well. He initiated a number of new research directions in analysis and differential geometry. Notable among these was his theory of reference systems, called "frametheory". This provides a crucial mathematical link between concepts from classical physics and the geometric language of general relativity, and it has been successfully used to understand the precise relations between the different ways that Newton´s and Einstein´s theories of gravity would describe the same physical system. This is a key question, because many of the tests of the correctness of general relativity rely on measuring some of the small ways in which motions in the Solar System differ from those expected on the basis of Newton's theory of gravity. Ehlers had a rare ability to formulate fundamental physical questions in a precise mathematical language. His influence on research on the mathematics of Einstein's equations will be felt for many years to come.
In 1990 Ehlers had what he later described as the one good political idea in his life: he proposed that the Max Planck Society should create a research institute dedicated to research on gravitation. The reunification of Germany had created a need to expand the Max Planck system into former East Germany, and Ehlers felt that an institute in Potsdam, near Berlin, would not only make sense scientifically but would also finally allow Germany to make a visible and practical repudiation of the Nazis' personal vilification of Einstein, which had driven Einstein away from Berlin and Germany and had completely stopped relativity research in Germany. He used his scientific prestige to open political doors, and the result was the opening in 1995 of the AEI in Potsdam.
His vision for the research scope of the AEI showed again his perceptiveness and interest in relativity as a whole, even in work that was far from his own research. He wanted all of relativity under one roof: astrophysical research into black holes and gravitational waves, mathematical research to keep providing rigourous answers to questions raised by astronomical discoveries, and research designed to lead finally to a quantum theory of gravity, the goal that had motivated the revival of relativity in the 1950s and which even today is still not met. Today the AEI actually has two roofs: its theory branch in Potsdam/Golm, and its experimental branch in Hannover, which operates the GEO600 gravitational wave detector and plays a key role in the development of future detectors on the ground and in space. Employing two hundred staff, hosting a further two hundred scientific visitors each year, housing some of the world's fastest supercomputers, operating the GEO600 detector, hosting numerous conferences and workshops, publishing its own scientific journal and editing others, the AEI amply justifies Ehlers' initial vision that relativity best makes progress by keeping all its subfields connected and in communication.
In recent years Ehlers spent more time pursuing his lifelong interests in the history of science and the meaning and importance of science to society. He engaged in public debates and wrote numerous articles. He strongly believed that rational thought and the scientific process were key ingredients of a civilised society, but he wanted society to understand the process as a human one, as an ongoing search for an ever deeper reality rather than as a way of manufacturing "laws" written in stone.
Naturally, Jürgen Ehlers won many honours in his lifetime: the Max Planck Medal from the German Physical Society in 2002, the Volta Gold Medal of Pavia University in the "Einstein Year" 2005, and recently the Chancellor's Medal of Charles University in Prague (2007). He was a member of BerlinBrandenburg Academy of Sciences, the Mainz Academy of Sciences and Literature, the Leopoldina, and the Bavarian Academy of Sciences. In 1995 his scientific colleagues elected him President of the International Society for General Relativity and Gravitation for three years. He was an Honorary Fellow of the InterUniversity Center for Astronomy & Astrophysics in Pune, India. But despite these honours and his considerable influence, Ehlers will be remembered by those who knew him as a modest man and a gentleman, a mentor who led by his example and by his deep scientific insight, a leader who always showed respect for his colleagues and coworkers.
Jürgen Ehlers will be deeply missed by his scientific colleagues, and of course incomparably more by the family he left behind: his wife Anita, his children Martin, Kathrin, David and Max, and five grandchildren.
The directors of the Albert Einstein Institute
Jürgens Ehlers Photo and Document Album 

