Jump to content

Jürgen Ehlers

From Wikipedia, the free encyclopedia

This is an old revision of this page, as edited by Markus Pössel (talk | contribs) at 17:29, 14 April 2013 (→Exact solutions: Fixing citation template). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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, Matthias Bartelmann

Jürgen Ehlers (December 29, 1929 – 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 lecture- 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 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, general-relativistic model universes to modern cosmology. He created a spacetime-oriented 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 popularizer of science.

Biography

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 in 1958.[1]

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 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 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 held teaching and research positions at the University of Kiel, Syracuse University and Hamburg University. In 1964, Ehlers again moved to the United States. 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 in 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' name 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' postdocs 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.[9]

Potsdam

When 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 gravitational theory. On June 9, 1994, the Society indeed decided to open a Max Planck Institute for Gravitational Physics in Potsdam. The institute started operations on April 1, 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 December 31, 1998, Ehlers retired to become founding director emeritus.[11] He continued to work at the institute until his death on May 20, 2008.[12]

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.[13]

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 general-relativistic 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.[14]

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".[15] The first paper, written with Jordan and Kundt, is a treatise on the properties and characteristics of exact solutions to Einstein's field equations. 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 space-time that are not constrained by Einstein's equations), isometry groups and conformal transformations. This work also includes the first definition and classification of pp-waves, a class of simple gravitational waves.[16]

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 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 result 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 essential for the discovery by Roy Kerr of his Kerr solution, describing a rotating black hole – one of the most important exact solutions.[17]

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, 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 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".[18]

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 evolve.[19]

Ehlers group

Main article: 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 field B electrodynamics: In the complete absence of electrical charges, the replacement E –B, B 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.[20]

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 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 . This larger symmetry group has since become known as the Ehlers group. Its discovery led to further generalizations, notably 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.[21]

Cosmology: Ehlers-Geren-Sachs theorem

Main article: 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, 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 Friedman-Lemaître spacetime.[22] Cosmic isotropy and homogeneity are important as they are the basis of the modern standard model of cosmology.[23]

Fundamental concepts in general relativity

In the 1960s, Ehlers collaborated with Felix Pirani and Alfred Schild 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, 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.[24]

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 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.[25]

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 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 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.[26] In the following years, Ehlers continued his research on the propagation of bundles of light in arbitrary spacetimes.[27]

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 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 Friedman-Lemaître models or the Gödel universe to be constructed.[28] 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, where Newtonian gravity is complemented by terms of ever higher order in in order to accommodate relativistic effects.[29]

General relativity is non-linear: 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 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, higher than were computed until then.[30]

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 non-linear consequence of inhomogeneities in general-relativistic cosmology.[31]

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.[32] In particular, he explored Pascual Jordan's seminal contributions to the development of quantum field theory between 1925 and 1928.[33] 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.[34]

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 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.[35] 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.[36]

Honours and awards

Ehlers 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).[37] From 1995 to 1998, he served as president of the International Society on General Relativity and Gravitation.[38] 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).[39]

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.[40] Issue 9 of volume 41 of the journal General Relativity and Gravitation was dedicated to Ehlers, in memoriam.[41]

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 3-540-66506-4

References

  1. ^ 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) and to Ellis, George, "Editorial note to: Pascual Jordan, Jürgen Ehlers, and Wolfgang Kundt, Exact solutions of the field equations of the general theory of relativity", General Relativity and Gravitation, 41 (9): 2170–2189, doi:10.1007/s10714-009-0868-9
  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; Sachs, Rainer, "Some memories of Juergen", General Relativity and Gravitation, 41 (9): 1903–1904, doi:10.1007/s10714-009-0784-z
  4. ^ Ellis, George, "Editorial note to: Pascual Jordan, Jürgen Ehlers, and Wolfgang Kundt, Exact solutions of the field equations of the general theory of relativity", General Relativity and Gravitation, 41 (9): 2170–2189, doi:10.1007/s10714-009-0868-9
  5. ^ 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).
  6. ^ Henning, Eckart and Marion Kazemi (2011), Chronik der Kaiser-Wilhelm-/Max-Planck-Gesellschaft zur Förderung der Wissenschaften 1911-2011, Berlin: Dunker & Humblot, p. 472
  7. ^ Henning, Eckart and Marion Kazemi (2011), Chronik der Kaiser-Wilhelm-/Max-Planck-Gesellschaft zur Förderung der Wissenschaften 1911-2011, Berlin: Dunker & Humblot, p. 634
  8. ^ Ashtekar: Abhay Ashtekar : Curriculum Vitae, Penn State University, 2007, retrieved 2008-05-27
  9. ^ Breuer has written about Ehlers, including remarks on his time in the Munich group, in the blog entry Breuer, Reinhard (2008-05-26), Jürgen Ehlers und die Relativitätstheorie, Spektrum der Wissenschaft Verlagsgesellschaft mbH (in German, English translation of title Jürgen Ehlers and the Theory of Relativity).
  10. ^ Henning, Eckart and Marion Kazemi (2011), Chronik der Kaiser-Wilhelm-/Max-Planck-Gesellschaft zur Förderung der Wissenschaften 1911-2011, Berlin: Dunker & Humblot, p. 676
  11. ^ Henning, Eckart and Marion Kazemi (2011), Chronik der Kaiser-Wilhelm-/Max-Planck-Gesellschaft zur Förderung der Wissenschaften 1911-2011, Berlin: Dunker & Humblot, p. 737
  12. ^ 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.
  13. ^ Schücking, Engelbert (2001), "Laudatio Jürgen Ehlers", Annual Report 2000 (PDF), Max Planck Institute for Gravitational Physics, pp. 46–47.
  14. ^ 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.
  15. ^ p. 2180 in Ellis, George, "Editorial note to: Pascual Jordan, Jürgen Ehlers and Wolfgang Kundt, Exact solutions of the field equations of the general theory of relativity", General Relativity and Gravitation, 41 (9): 2170–2189, doi:10.1007/s10714-009-0868-9
  16. ^ 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.
  17. ^ Ehlers-Sachs theorem see sec. 5.3 in Frolov, Valeri P.; Novikov, I. D. (1997), Black Hole Physics, Kluwer. 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", Akad. Wiss. Lit. Mainz, Abh. Naturwiss. Kl., 1 (in German, English translation of title: Contributions to the theory of pure gravitational radiation).
  18. ^ The paper 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 (12): 1225–1266, Bibcode:1993GReGr..25.1225E, doi:10.1007/BF00759031 (for the journal's "Golden Oldies" section); quotation on p. 1225.
  19. ^ 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).
  20. ^ E.g. Olive, D. I. (1996), "Exact Electromagnetic Duality", Nucl. Phys. B (Proc. Suppl), 45A (1): 88–102, arXiv:hep-th/9508089, Bibcode:1996NuPhS..45...88O, doi:10.1016/0920-5632(95)00618-4
  21. ^ 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 (6): 918–924, Bibcode:1971JMP....12..918G, 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 (4): 719–738, arXiv:gr-qc/0101020, Bibcode:2001CQGra..18..719M, doi:10.1088/0264-9381/18/4/311.
  22. ^ Hawking, Stephen W.; Ellis, George F. R. (1973), The large scale structure of space-time, Cambridge University Press, pp. 351ff, ISBN 0-521-09906-4. The original work is Ehlers, J., Geren, P., Sachs, R.K.: Isotropic solutions of Einstein-Liouville equations. J. Math. Phys. 9, 1344 (1968)
  23. ^ Andrew Liddle (2003). An Introduction to Modern Cosmology (2nd ed.). John Wiley & Sons. ISBN 978-0-470-84835-7., p. 2
  24. ^ 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
  25. ^ See Köhler, Egon; Schattner, Ruprecht (1979), "Some results on pseudorigid motions", General Relativity and Gravitation, 10 (8): 709–716, Bibcode:1979GReGr..10..709K, doi:10.1007/BF00756906. 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 (3): 197–217, Bibcode:1977GReGr...8..197E, doi:10.1007/BF00763547.
  26. ^ Cf. the review Bleyer, U. (1993), "Book-Review - Gravitational Lenses", Astronomische Nachrichten, 314: 314–315, Bibcode:1993AN....314..314S. 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 (2): 435–436, Bibcode:2005GReGr..37..435P, 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 (7): 1335–1336, Bibcode:2005GReGr..37.1335B, doi:10.1007/s10714-005-0117-9.
  27. ^ Seitz, S.; Schneider, P.; Ehlers, J. (1994), "Light propagation in arbitrary spacetimes and the gravitational lens approximation", Class. Quantum Grav., 11 (9): 2345–2383, arXiv:astro-ph/9403056, Bibcode:1994CQGra..11.2345S, doi:10.1088/0264-9381/11/9/016, cf. section 3.5 of Annual Report 1994, Max Planck Institute for Astrophysics, 1995
  28. ^ Cf. Ehlers, J. (1997), "Examples of Newtonian limits of relativistic spacetimes", Classical and Quantum Gravity, 14 (1A): A119–A126, Bibcode:1997CQGra..14A.119E, 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.
  29. ^ Olinyk, Schmidt Oliynyk, Todd Andrew; Schmidt, Bernd, "Existence of families of spacetimes with a Newtonian limit", General Relativity and Gravitation, 41 (9): 2093–2111, doi:10.1007/s10714-009-0843-5
  30. ^ A description that includes 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 (3–4): 183–197, Bibcode:1996JApA...17..183S, 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).
  31. ^ 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, arXiv:astro-ph/9510056, Bibcode:1997A&A...320....1B, and Buchert, Thomas; Ehlers, Jürgen (1997f), "Newtonian cosmology in Lagrangian formulation: foundations and perturbation theory", General Relativity and Gravitation, 29 (6): 733–764, arXiv:astro-ph/9609036, Bibcode:1997GReGr..29..733E, 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 (2–3): 467–527, arXiv:0707.2153, Bibcode:2008GReGr..40..467B, doi:10.1007/s10714-007-0554-8
  32. ^ 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.
  33. ^ 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)
  34. ^ 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; English translation in Breuer, Reinhard; Springer, Michael, "The truth in science", General Relativity and Gravitation, 41 (9): 2159–2167, doi:10.1007/s10714-009-0844-4 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).
  35. ^ 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
  36. ^ 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).
  37. ^ 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).
  38. ^ GRG Society History, Website of the International Society on General Relativity and Gravitation, retrieved 2008-05-27.
  39. ^ 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).
  40. ^ Ehlers prize, Website of the International Society on General Relativity and Gravitation, retrieved 2012-10-02
  41. ^ Nicolai, Hermann; Ellis, George; Schmidt, Bernd (2009), "Editorial", General Relativity and Gravitation, 41 (9), doi:10.1007/s10714-009-0867-x

Template:German

Template:Persondata

Retrieved from "https://en.wikipedia.org/w/index.php?title=Jürgen_Ehlers&oldid=550336810"