Jürgen Ehlers

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Jürgen Ehlers
At the award ceremony for the Charles University Medal in Potsdam, September 2007
Born(1929-11-29)November 29, 1929
Hamburg
DiedMay 20, 2008(2008-05-20) (aged 78)
Potsdam, Germany
NationalityGerman
Alma materUniversity of Hamburg
Known forGeneral relativity
Mathematical physics
AwardsMax Planck Medal (2002)
Scientific career
FieldsPhysics
InstitutionsUniversity of Hamburg
Max Planck Institute for Astrophysics
Max Planck Institute for Gravitational Physics
Doctoral advisorPascual Jordan
Doctoral studentsThomas Buchert

Jürgen Ehlers (December 29, 1929 – May 20, 2008) was a German physicist who made notable contributions to the current understanding of Albert Einstein's theory of general relativity. From graduate and postgraduate work in Pascual Jordan's relativity group at Hamburg University, he moved on to various lecturer- and professorships 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 (Albert Einstein Institute) in Potsdam, Germany.

Ehlers' research focused on the foundations of general relativity, as well as its applications to various areas astrophysics. In particular, he is notable for his work on the classification of exact solutions to Einstein's field equations, for the Ehlers-Geren-Sachs theorem that justifies the application of simple, general-relativistic model universes to modern cosmology, for a spacetime-oriented description of gravitational lensing, and for his work on 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 popularizer of science.

Biography

Early career

Jürgen Ehlers was born in Hamburg. He attended public schools from 1936 to 1949, and 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 examen, but went on to graduate research in the group of Pascual Jordan, with Jordan acting as his thesis advisor. His work on the construction and characterization of solutions of the Einstein field equations earned him a doctorate in 1958.[1] While earlier, the main research of Jordan's group had been dedicated to a scalar-tensor modification of Einstein's theory of general relativity, now known as Jordan-Brans-Dicke theory, in which the gravitational constant is variable, 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, Engelbert Schücking, Otto Heckmann, Rainer Sachs, and Manfred Trümper.[3]

In 1961, having become Jordan's assistant, Ehlers obtained his habilitation, the advanced degree that, by the rules of German academia, qualifies the bearer for a professorship. He then held teaching and research positions at the University of Kiel, Syracuse University, and Hamburg University, before once more moving to the United States: from 1964 to 1965, he was at the Graduate Research Center of the Southwest in Dallas, and from 1965 to 1971 at the University of Texas in Austin, joining Alfred Schild's group first as an associate professor and, from 1967 on, as a full professor of physics. During that time, he also held visiting professorships at the universities of Würzburg and Bonn.[4]

Munich

In 1971, Ehlers received an offer to join the Max Planck Institute for Physics and Astrophysics in Munich, one of the institutes of Germany's major organization for basic research, the Max Planck Society, as the director of its gravitational theory department. Ehlers' name had been brought into play by Ludwig Biermann, the institute's director at the time. Ehlers accepted, and also became an adjunct professor at Munich's Ludwig Maximilian University. In 1991, the institute was split into the Max Planck Institute for Physics and the Max Planck Institute for Astrophysics, where Ehlers' department found a new home. 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.[5] One of Ehlers' post-docs in Munich was Reinhard Breuer, who would later go on to become the editor-in-chief of Spektrum der Wissenschaft, the German edition of the popular-science journal Scientific American.[6]

Potsdam

As German science institutions reorganized after German re-unification in 1990, Ehlers lobbied for the establishment of an institute of the Max Planck Society dedicated to research on Einstein's theories of gravity. He was successful, and became the founding director of the Max Planck Institute for Gravitational Physics in Potsdam in 1995, as well as the leader of its department for the foundations and mathematics of general relativity. He also oversaw the funding of a second institute department devoted to gravitational wave research and headed by Bernard F. Schutz. In the beginning of 1999, Ehlers retired to become founding director emeritus. He continued to work at the institute until his death on May 20, 2008.[7]

Honours and awards

In the course of his career, Ehlers received various awards and honours. He became a member of the Berlin-Brandenburgische Akademie der Wissenschaften, 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).[8] From 1995 to 1998, he served as president of the International Society on General Relativity and Gravitation.[9] 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).[10]

Work

Ehlers' research was in the field of general relativity. In particular, he made important contributions to cosmology, the theory of gravitational lenses and gravitational waves. His principal concern was to clarify the theory's mathematical structure and its consequences, separating rigorous proofs from heuristic conjectures.[11]

Exact solutions

For his doctoral thesis, Ehlers turned to a question that was to shape his research far beyond his graduate studies. Exact solutions of Einstein's equations – in effect, universes consistent with the laws of general relativity which are simple enough to allow for an explicit description in terms of basic mathematical expressions – play a key role when it comes to building general-relativistic models. 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 to Einstein's equations could, in fact, correspond the same model universe, and differ only in the coordinates used in their description. Ehlers began to look for serviceable ways of characterizing exact solutions invariantly, that is, in ways that do not depend on the choice of coordinates. To this end, he examined ways of describing the intrinsic geometric properties of the known exact solutions.[12]

During the 1960s, following up on the groundwork of research for his doctoral thesis, Ehlers published a series of seminal papers, all but one in collaboration with colleagues from the Hamburg group. The first, written with Jordan and Wolfgang Kundt, is a systematic exposition of the properties and characteristics of exact solutions to Einstein's field equations, using tools from differential geometry such as the Petrov classification of Weyl tensors (that is, those parts of the Riemann tensor describing the curvature of space-time which are not constrained by Einstein's equations), isometry groups, and conformal transformations. This work also includes the first definition of pp-waves, a class of especially simple gravitational waves, as well as their classification.[13] There were also two treatises on gravitational radiation (one with Rainer Sachs, one with Manfred Trümper). The work with Sachs studies, among other things, vacuum solutions with special algebraic properties, using the 2-component spinor formalism. It also gives a systematic exposition of the geometric properties of bundles (congruences) of light beams in terms of their expansion (simply put, how the beams converge or diverge), twist and shear (how, apart from growing or shrinking, the cross section is deformed). One of the results is the Ehlers-Sachs theorem describing the properties of the shadow produced by a narrow beam of light passing an opaque object. The tools developed in that work would prove to be essential for the discovery by Roy Kerr of the Kerr solution, describing a rotating black hole – arguably the most important exact solution of all.[14] The last of these seminal papers dealt with the general-relativistic treatment of the mechanics of continuous media.[15]

Another part of Ehlers' exploration of exact solutions in his thesis led to a result that would later prove to be important. At the time Ehlers started his research on his doctoral thesis, the Golden age of general relativity had not quite 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 with time.[16]

Ehlers group

In physics, a duality symmetry is said to exist whenever the laws of physics remain unchanged under the exchange of seemingly different physical quantities. The best-known example is the duality between the electric field E and the magnetic field field B in source-free electrodynamics, where the replacement E –B, B E leaves Maxwell's equations invariant.[17]

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 tt-component of the metric and a term known as the twist potential is analogous to This duality was later generalized to an symmetry which became known as the Ehlers group. Further generalizations led to the discovery of the infinite-dimensional Geroch group (the Geroch group is generated by two non-commuting subgroups, 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. 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 case form an integrable system.[18]

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 Kelvin.

The Ehlers-Geren-Sachs theorem, published in 1968 by Ehlers, P. Geren and Rainer Sachs, shows that if, in a given universe, 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 FLRW spacetime.[19]

Fundamental concepts in general relativity

Throughout his research career, Ehlers never lost sight of the fundamental concepts of Einstein's theory. In the 1960s, he collaborated with Felix Pirani and Alfred Schild on a constructive-axiomatic approach to general relativity: a way of deriving Einstein's theory from a minimal set of elementary objects and axioms specifying their 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. By postulating the basic properties of light and freely falling particles as axioms, the differential topology, conformal structure and, finally, the metric structure of spacetime are constructed; key steps of the construction correspond to idealized measurements, such the standard range finding used in radar. As the final step, Einstein's equations are derived from the weakest possible set of additional axioms. The result is a formulation in which the assumptions underlying general relativity are clearly identified.[20]

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, but the fact that their different parts by definition 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. As early as 1909, Max Born had given a definition of rigidity that was compatible with relativistic physics. However, this definition depends on certain assumptions that are not satisfied in a general space-time, and are also 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 rigidiy of classical physics.[21]

Gravitational lensing

Most astrophysical modeling of gravitational lens systems makes use of the quasi-Newtonian approximation

With Peter Schneider, Ehlers embarked on an in-depth study of the foundations of gravitational lensing. One result of this work was an 1992 monograph co-authored with both Schneider and Emilio Falco: the first systematic exposition of the field that included both the theoretical foundations and observational results. From the viewpoint of astronomy, gravitational lensing is often described using a quasi-Newtonian 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 space-time perspective. This feature of the book has played a major part in the book's long-term positive reception.[22] In the following years, Ehlers continued his research on the propagation of bundles of light in arbitrary spacetimes.[23]

Frame theory and Newtonian gravity

A basic derivation of the Newtonian limit of general relativity is as old as the theory itself, and was used by Einstein to derive predictions such as the anomalous perihelion precession of the planet Mercury. Later work by Elie 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, obtained by letting a specific parameter go to zero. Ehlers extended this work by developing a frame theory, a mathematically precise way of constructing the Newton-Cartan limit not only of the physical laws of general relativity, but of any spacetime obeying those laws, that is, of any solution to Einstein's equations. For instance, this can be used to show that the Newtonian limit of a Schwarzschild black hole is a simple point particle; in addition, Newtonian versions of interesting exact solutions such as the Friedman-Lemaître models or the Gödel universe can be constructed.[24]

Ehlers also took part 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 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 higher-order terms than was commonly assumed, and in fact higher terms than were computed until then.[25]

His work on the Newtonian limit, in particular in relation to cosmological solutions, also 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 general-relativistic generalization of this treatment of inhomogeneities, 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 non-linear consequence of inhomogeneities in general-relativistic cosmology.[26]

History and philosophy of physics

Complementing his interest in the foundations of general relativity and, more generally, of physics, Ehlers also did research on 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.[27] In particular, he explored Pascual Jordan's seminal contributions to the development of quantum field theory between 1925 and 1928.[28] 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.[29]

Communicating science

Ehlers showed a keen interest in communicating his area of research to a general audience. He was a frequent public lecturer, at universities as well as at venues such as the Urania in Berlin. He is the author of a number of popular-science articles, including contributions to general-audience journals such as Bild der Wissenschaft. and also edited a compilation of articles on gravity from the German edition of Scientific American.[30] Ehlers also directly addressed physics teachers, be it in talks or in journal articles on the teaching of relativity and related basic ideas of physics, such as on mathematics as the language of physics.[31]

Selected publications

  • Börner, G.; Ehlers, J., eds. (1996), Gravitation, Spektrum Akademischer Verlag, ISBN 3-86025-362-X
  • Ehlers, Jürgen (1973), "Survey of general relativity theory", in Israel, Werner (ed.), Relativity, Astrophysics and Cosmology, D. Reidel, pp. 1–125, ISBN 90-277-0369-8
  • Schneider, P.; Ehlers, J.; Falco, E. E. (1992), Gravitational lenses, Springer, ISBN 3540665064

References

  1. ^ According to the brief biography appended to Ehlers' dissertation, Ehlers, Jürgen (1957), Konstruktionen und Charakterisierungen von Lösungen der Einsteinschen Gravitationsfeldgleichungen, University of Hamburg (in German, title in English translation: Constructions and characterizations of solutions to Einstein's gravitational field equations).
  2. ^ Schücking, Engelbert (2006), "Jürgen Ehlers", in Schmidt, Bernd G. (ed.), Einstein's Field Equations and Their Physical Implications, Springer, pp. V–VI
  3. ^ Ellis, George; Krasiński, Andrzej (2007), "Editors' comment", General Relativity and Gravitation, 39: 1941–1942
  4. ^ As detailed in the obituary Prof. Dr. Jürgen Ehlers ist verstorben. Das Albert-Einstein-Institut trauert um seinen Gründungsdirektor (PDF), Max Planck Institute for Gravitational Physics, May 27, 2008, retrieved 2008-05-27 (in German, title in English translation: Prof. Jürgen Ehlers has died. The Albert Einstein Institute mourns for its founding director), and the associated CV, Lebenslauf von Prof. Dr. Jürgen Ehlers (PDF), Max Planck Institute for Gravitational Physics, May 27, 2008, retrieved 2008-05-27 (in German, English translation of title: "CV for Prof. Dr. Jürgen Ehlers"). Dates and positions also summarized in Weber, Peter; Borissoff, Irene, eds. (1998), Handbuch der Wissenschaftlichen Mitglieder, Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V., p. 38 (in German, English translation of title: Handbook of Scientific Members).
  5. ^ Ashtekar: Abhay Ashtekar : Curriculum Vitae, Penn State University, 2007, retrieved 2008-05-27
  6. ^ Breuer has written about Ehlers, including remarks on his time in the Munich group, in the blog entry Jürgen Ehlers und die Relativitätstheorie, Spektrum der Wissenschaft Verlagsgesellschaft mbH, 2008-05-26, p. Breuer {{citation}}: |first= missing |last= (help) (in German, English translation of title Jürgen Ehlers and the Theory of Relativity).
  7. ^ See p. 520 in the Max Planck Society's annual report for 2000, Jahrbuch 2000, Max-Planck-Gesellschaft, 2000. Time as emeritus and death: Braun, Rüdiger (May 27, 2008), "Wo Zeit und Raum aufhören. Der Mitbegründer des Golmer Max-Planck-Instituts für Gravitationsphysik, Jürgen Ehlers, ist unerwartet verstorben", Märkische Allgemeine Zeitung, retrieved 2008-05-27 (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). Details about the project can be found on its website.
  8. ^ Berlin: Members/staff, Berliner Akademiegeschichte im 19. und 20. Jahrhundert, Berlin-Brandenburgische Akademie der Wissenschaften, retrieved 2008-05-27. Mainz: Mitglieder E, Website of Akademie der Wissenschaften und der Literatur, Mainz, retrieved 2008-05-27 (in German, English translation of title: Members). Leopoldina: listed as member on Mitgliederverzeichnis, Deutsche Akademie der Naturforscher Leopoldina, August 20, 2007, retrieved 2008-05-27 (in German, English translation of title: Members list). Bavarian Academy: Listed as corresponding member in Bayerische Akademie der Wissenschaften - Kompetenzen (PDF), Bayerische Akademie der Wissenschaften, 2006, p. 166, retrieved 2008-05-27 (in German, English translation of title: Bavarian Academy of Sciences - Experts).
  9. ^ GRG Society History, Website of the International Society on General Relativity and Gravitation, retrieved 2008-05-27.
  10. ^ Max Planck Medal: Press release about the 2002 awards, Physikalische Spitzenleistung, Deutsche Physikalische Gesellschaft, December 17, 2001, retrieved 2008-05-27 (in German, English translation of title: Top achievement in physics) and Rogalla, Thomas (December 28, 2001), "Namen: Prof. Dr. Jürgen Ehlers", Berliner Zeitung, retrieved 2008-05-27 (in German). Volta Medal: "Namen: Prof. Dr. Jürgen Ehlers", Berliner Zeitung, May 18, 2005, retrieved 2008-05-27 (in German) and "Medaille für Golmer Forscher", Märkische Allgemeine Zeitung, May 19, 2005 (in German, English translation of title: Medal for researcher from Golm).
  11. ^ Schücking, Engelbert (2001), "Laudatio Jürgen Ehlers", Annual Report 2000 (PDF), Max Planck Institute for Gravitational Physics, pp. 46–47.
  12. ^ Schmidt, Bernd (2000), "Preface", in Schmidt, B. (ed.), Einstein's Field Equations and their Physical Implications. Selected Essays in Honour of Jürgen Ehlers, Springer, pp. 1–126, ISBN 3-540-67073-4.
  13. ^ A later version of this paper is Ehlers, Jürgen; Kundt, Wolfgang (1962), "Exact Solutions of the Gravitational Field Equations", in Witten, Louis (ed.), Gravitation: An Introduction to Current Research, New York: John Wiley & Sons, pp. 49–101. For an assessment, see p. 14f. in Bicak, Jiri (2000), Schmidt, B. (ed.), Einstein's Field Equations and their Physical Implications. Selected Essays in Honour of Jürgen Ehlers, Springer, pp. 1–126, ISBN 3-540-67073-4.
  14. ^ Ehlers-Sachs theorem see sec. 5.3 in Frolov, Valeri P.; Novikov, I. D. (1997), Black Hole Physics, Kluwer {{citation}}: Check |author2-link= value (help). Assessment of the work and connection with Kerr solution as described on p. 14f. of Bicak, Jiri (2000), Schmidt, B. (ed.), Einstein's Field Equations and their Physical Implications. Selected Essays in Honour of Jürgen Ehlers, Springer, pp. 1–126, ISBN 3-540-67073-4. The original work with Sachs is Jordan, P.; Ehlers, J.; Sachs, R. K. (1961), Beiträge zur Theorie der reinen Gravitationsstrahlung, vol. 1 {{citation}}: Unknown parameter |unused_data= ignored (help) (in German, English translation of title: Contributions to the theory of pure gravitational radiation).
  15. ^ It was translated into English by G. F. R. Ellis as Ehlers, J. (1993), "Contributions to the relativistic mechanics of continuous media", Gen. Rel. Grav., 25: 1225–1266, doi:10.1007/BF00759031 (for the journal's "Golden Oldies" section)
  16. ^ The changing views of what eventually be regarded as black holes can be found in Israel, Werner (1987), "Dark stars: the evolution of an idea", in Hawking, Stephen W.; Israel, Werner (eds.), 300 Years of Gravitation, Cambridge University Press, pp. 199–276, ISBN 0-521-37976-8. Ehlers' thesis is Ehlers, Jürgen (1957), Konstruktionen und Charakterisierungen von Lösungen der Einsteinschen Gravitationsfeldgleichungen, University of Hamburg (in German, English translation of title: Constructions and characterizations of solutions of Einstein's gravitational field equations).
  17. ^ E.g. Olive, D. I. (1996), "Exact Electromagnetic Duality", Nucl. Phys. B (Proc. Suppl), 45A: 88–102, doi:10.1016/0920-5632(95)00618-4
  18. ^ As described in Maison, Dieter (2006), "Duality and Hidden Symmetries in Gravitational Theories", in Schmidt, Bernd G. (ed.), Einstein's Field Equations and Their Physical Implications, Springer, pp. 273–323, ISBN 3-540-67073-4. For the generalizations, see Geroch, R. (1971), "A method for generating new solutions of Einstein's field equation. I", J. Math. Phys., 12: 918–924, doi:10.1063/1.1665681; for the applications, Mars, Marc (2001), "Space-time Ehlers group: Transformation law for the Weyl tensor", Class. Quant. Grav., 18: 719–738, doi:10.1088/0264-9381/18/4/311.
  19. ^ Ehlers, J., Geren, P., Sachs, R.K.: Isotropic solutions of Einstein-Liouville equations. J. Math. Phys. 9, 1344 (1968)
  20. ^ Ehlers, Jürgen; Pirani, F. A. E.; Schild, Alfred (1972), O'Raifeartaigh, L. (ed.), General Relativity, Clarendon Press, p. 63; a summary can be found in Ehlers, Jürgen (1973), "Survey of general relativity theory", in Israel, Werner (ed.), Relativity, Astrophysics and Cosmology, D. Reidel, pp. 1–125, ISBN 90-277-0369-8
  21. ^ See Köhler, Egon; Schattner, Ruprecht (1979), "Some results on pseudorigid motions", General Relativity and Gravitation, 10: 709–716, doi:10.1007/BF00756906{{citation}}: CS1 maint: multiple names: authors list (link). The original publication is Ehlers, Jürgen; Rudolph, Ekkart (1977), "Dynamics of extended bodies in general relativity center-of-mass description and quasirigidity", General Relativity and Gravitation, 8: 197–217, doi:10.1007/BF00763547.
  22. ^ Cf. the review Bleyer, U. (1993), "Book-Review - Gravitational Lenses", Astronomische Nachrichten, 314: 314–315. For the long-term perspective, cf. the mention the monograph receives in the reviews of much more recent works on gravitational lensing, such as Perlick, Volker (2005), "Book review:Petters, A.O., Levine, H., Wambsganss, J.: Singularity theory and gravitational lensing", Gen. Relativ. Gravit., 37: 435–436, doi:10.1007/s10714-005-0033-z and Bozza, Valerio (2005), "Book review: Silvia Mollerach, Esteban Roulet: Gravitational Lensing and Microlensing", General Relativity and Gravitation, 37: 1335–1336, doi:10.1007/s10714-005-0117-9.
  23. ^ Seitz, S.; Schneider, P.; Ehlers, J. (1994), "Light propagation in arbitrary spacetimes and the gravitational lens approximation", Class. Quantum Grav., 11: 2345–2383, doi:10.1088/0264-9381/11/9/016, cf. section 3.5 of Annual Report 1994, Max Planck Institute for Astrophysics, 1995
  24. ^ Cf. Ehlers, J. (1997), "Examples of Newtonian limits of relativistic spacetimes", Classical and Quantum Gravity, 14: A119–A126, doi:10.1088/0264-9381/14/1A/010; a description can be found on p. 216f. in Blanchet, Luc (2006), "Post-Newtonian Gravitational Radiation", in Schmidt, Bernd G. (ed.), Einstein's Field Equations and Their Physical Implications, Springer, pp. 225–271, ISBN 3-540-67073-4.
  25. ^ A description that include the historical context can be found in Schutz, B. F. (1996), "Making the Transition from Newton to Einstein: Chandrasekhar's Work on the Post-Newtonian Approximation and Radiation Reaction" (PDF), J. Astrophys. Astr., 17: 183–197, doi:10.1007/BF02702303. The original work is Ehlers, J.; Rosenblum, A.; Goldberg, J. N.; Havas, Peter, Astrophys. J., 208: L77 {{citation}}: Missing or empty |title= (help).
  26. ^ Buchert, Thomas; Ehlers, Jürgen (1993), "Lagrangian theory of gravitational instability of Friedmann-Lemaître cosmologies – second-order approach: an improved model for nonlinear clustering", Mon. Not. R. Astron. Soc., 264: 375, Buchert, Thomas; Ehlers, Jürgen (1997), "Averaging inhomogeneous Newtonian cosmologies", Astron. Astrophys., 320: 1–7, and Buchert, Thomas; Ehlers, Jürgen (1997f), "Newtonian cosmology in Lagrangian formulation: foundations and perturbation theory", General Relativity and Gravitation, 29: 733–764, doi:10.1023/A:1018885922682. The current status of Buchert's further work is summarized in Buchert, Thomas (2007), "Dark Energy from Structure—A Status Report", General Relativity and Gravitation, 40: 467–527, doi:10.1007/s10714-007-0554-8, arXiv:0707.2153
  27. ^ E.g. Braun, Rüdiger (May 27, 2008), "Wo Zeit und Raum aufhören. Der Mitbegründer des Golmer Max-Planck-Instituts für Gravitationsphysik, Jürgen Ehlers, ist unerwartet verstorben", Märkische Allgemeine Zeitung, retrieved 2008-05-27 (in German, English translation of title: Where time and space end. The co-founder of the Max Planck Institute for Gravitational Physics in Golm, Jürgen Ehlers, has died unexpectedly). Details about the project can be found on its website.
  28. ^ Ehlers, Jürgen (2007), "Pascual Jordan's Role in the Creation of Quantum Field Theory", in Ehlers, J.; Hoffmann, D.; Renn, Jürgen (eds.), Pascual Jordan (1902–1980). Mainzer Symposium zum 100. Geburtstag. Preprint Nr. 329, Max Planck Institute for the History of Science, pp. 23–35 {{citation}}: line feed character in |contribution= at position 42 (help)
  29. ^ Ehlers' work on the status of scientific knowledge e.g. Ehlers, Jürgen (2006), "Physikalische Erkenntnis, dargestellt am Beispiel des Übergangs von Newtons Raumzeit zu Einsteins spezieller Relativitätstheorie", in Balsinger, Philipp W.; Kötter, Rudolf (eds.), Die Kultur moderner Wissenschaft am Beispiel Albert Einstein, Elsevier/Spektrum Akademie Verlag, pp. 1–16 (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) and Breuer, Reinhard; Springer, Michael (2001), "Die Wahrheit in der Wissenschaft", Spektrum der Wissenschaft, 7: 70 (in German, English translation of title: Truth in science). Also Ehlers, Jürgen (2005), "Modelle in der Physik", Modelle des Denkens, Berlin-Brandenburgische Akademie der Wissenschaften, pp. 35–40 (in German, English translation of contribution title: Models in physics; English translation of title: Models of thinking).
  30. ^ Public lectures: Biennial Report 2004/2005 (PDF), Max Planck Institute for Gravitational Physics, 2006, lists 25 popular talks (p. 158f.) for that time-frame alone. The compilation of articles is Börner & Ehlers 1996, listed under Selected Publications. Popular articles e.g. Ehlers, J.; Fahr, H. J. (1994), "Urknall oder Ewigkeit", Bild der Wissenschaft, June: 84
  31. ^ Biennial Report 2004/2005 (PDF), Max Planck Institute for Gravitational Physics, 2006 lists 11 talks to teachers or in an interdisciplinary setting (p. 147f., p. 154f.). Mathematics and physics: Ehlers, Jürgen (2006), "Mathematik als „Sprache" der Physik", Praxis der Naturwissenschaften – Physik in der Schule, 55 (in German, English translation of title: Mathematics as the "language" of physics).

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