# Jürgen Ehlers

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Jürgen Ehlers

Infobox_Scientist
box width = 300px
name = Jürgen Ehlers
caption = At the award ceremony for the Charles University Medal in Potsdam, September 2007

imagesize = 138
birth_date = birth date|1929|11|29|mf=y
birth_place = Hamburg
residence = Germany
nationality = German
death_date = death date and age|2008|5|20|1929|11|29
death_place = Potsdam, Germany
field = Physics
work_institutions = University of Hamburg Max Planck Institute for Astrophysics Max Planck Institute for Gravitational Physics
alma_mater = University of Hamburg
doctoral_students = Thomas Buchert
known_for = General relativity Mathematical physics
prizes = Max Planck Medal (2002)
religion =

footnotes =

Jürgen Ehlers (December 29, 1929May 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

J&uuml;rgen Ehlers was born on December 29,1929 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. [According to the brief biography appended to Ehlers' dissertation, Citation
last=Ehlers
first=Jürgen
title=Konstruktionen und Charakterisierungen von Lösungen der Einsteinschen Gravitationsfeldgleichungen
publisher=University of Hamburg
year=1957
(in German, title in English translation: "Constructions and characterizations of solutions to Einstein's gravitational field equations").
] 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. [Citation|last=Schücking|first=Engelbert|contribution=Jürgen Ehlers|editor-last=Schmidt|editor-first=Bernd G.|title=Einstein's Field Equations and Their Physical Implications|year=2006|publisher=Springer|pages=V–VI] Other members of the group included Wolfgang Kundt, Engelbert Schücking, Otto Heckmann, Rainer Sachs, and Manfred Trümper. [Citation|last=Ellis|first=George|last2=Krasiński|first2=Andrzej|title=Editors' comment|journal=General Relativity and Gravitation|volume=39|year=2007|pages=1941–1942|url=http://edoc.mpg.de/335066]

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. [As detailed in the obituary Citation|title=Prof. Dr. Jürgen Ehlers ist verstorben. Das Albert-Einstein-Institut trauert um seinen Gründungsdirektor|publisher=Max Planck Institute for Gravitational Physics|date=May 27, 2008|year=2008|url=http://www.aei.mpg.de/pdf/pm_news/2008/Ehlers_Nachruf.pdf|access-date=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, Citation|title=Lebenslauf von Prof. Dr. Jürgen Ehlers|publisher=Max Planck Institute for Gravitational Physics|date=May 27, 2008|year=2008|url=http://www.aei.mpg.de/pdf/pm_news/2008/Ehlers_Lebenslauf.pdf|access-date=2008-05-27 (in German, English translation of title: "CV for Prof. Dr. Jürgen Ehlers"). Dates and positions also summarized in Citation|editor-last=Weber|editor-first=Peter|editor2-last=Borissoff|editor2-first=Irene|publisher=Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V.|title=Handbuch der Wissenschaftlichen Mitglieder|page=38|year=1998 (in German, English translation of title: "Handbook of Scientific Members").]

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. [Ashtekar: Citation|title=Abhay Ashtekar : Curriculum Vitae|publisher=Penn State University|url=http://cgpg.gravity.psu.edu/people/Ashtekar/cv.html|access-date=2008-05-27|year=2007] 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. [Breuer has written about Ehlers, including remarks on his time in the Munich group, in the blog entry Citation|name=Breuer|first=Reinhard|title=Jürgen Ehlers und die Relativitätstheorie|date=2008-05-26|publisher= Spektrum der Wissenschaft Verlagsgesellschaft mbH|url=http://www.wissenslogs.de/wblogs/blog/forschern-auf-der-spur/physik/2008-05-26/j-rgen-ehlers-und-die-relativit-tstheorie|year=2008 (in German, English translation of title "Jürgen Ehlers and the Theory of Relativity").]

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. [See p. 520 in the Max Planck Society's annual report for 2000, Citation|title=Jahrbuch 2000|publisher=Max-Planck-Gesellschaft|year=2000|url=http://www.mpg.de/english/illustrationsDocumentation/documentation/jahrbuch/2000/index.html. Time as emeritus and death: Citation|last=Braun|first=Rüdiger|title=Wo Zeit und Raum aufhören. Der Mitbegründer des Golmer Max-Planck-Instituts für Gravitationsphysik, Jürgen Ehlers, ist unerwartet verstorben|newspaper=Märkische Allgemeine Zeitung|date=May 27, 2008|url=http://www.maerkischeallgemeine.de/cms/beitrag/11216020/60709/Der_Mitbegruender_des_Golmer_Max_Planck_Instituts_fuer.html|year=2008|access-date=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 [http://quantum-history.mpiwg-berlin.mpg.de/ website] .]

Honours and awards

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. [Citation|last=Schücking|first=Engelbert|contribution=Laudatio Jürgen Ehlers|title=Annual Report 2000|publisher=Max Planck Institute for Gravitational Physics|pages=46–47|url=http://www.aei.mpg.de/pdf/illustrationsDocs/annual2000.pdf|year=2001.]

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. [Citation|last=Schmidt|first=Bernd|contribution=Preface|pages=VII–VIII|editor-last=Schmidt|editor-first=B.|pages=1–126|title=Einstein's Field Equations and their Physical Implications. Selected Essays in Honour of Jürgen Ehlers|publisher=Springer|isbn=3-540-67073-4.]

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. [A later version of this paper is Citation
last=Ehlers
first=Jürgen
last2=Kundt
first2=Wolfgang
contribution=Exact Solutions of the Gravitational Field Equations
title=Gravitation: An Introduction to Current Research
editor-last=Witten
editor-first=Louis
location=New York
publisher=John Wiley & Sons
year=1962
pages=49–101
. For an assessment, see p. 14f. in Citation|last=Bicak|first=Jiri|contribution=|editor-last=Schmidt|editor-first=B.|pages=1–126|title=Einstein's Field Equations and their Physical Implications. Selected Essays in Honour of Jürgen Ehlers|publisher=Springer|isbn=3-540-67073-4.
] 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. [Ehlers-Sachs theorem see sec. 5.3 in Citation|last=Frolov|first=Valeri P.|last2=Novikov|first2=I. D.|author2-link=Igor Dmitriyevich Novikov|title=Black Hole Physics|publisher=Kluwer|year=1997. Assessment of the work and connection with Kerr solution as described on p. 14f. of Citation|last=Bicak|first=Jiri|contribution=|editor-last=Schmidt|editor-first=B.|pages=1–126|title=Einstein's Field Equations and their Physical Implications. Selected Essays in Honour of Jürgen Ehlers|publisher=Springer|isbn=3-540-67073-4. The original work with Sachs is Citation|last=Jordan|first=P.|last2=Ehlers|first2=J.|last3=Sachs|first3=R. K.|year=1961|title=Beiträge zur Theorie der reinen Gravitationsstrahlung|Akad. Wiss. Lit. Mainz, Abh. Naturwiss. Kl.|volume=1 (in German, English translation of title: "Contributions to the theory of pure gravitational radiation").] The last of these seminal papers dealt with the general-relativistic treatment of the mechanics of continuous media. [It was translated into English by G. F. R. Ellis as Citation|last=Ehlers|first=J.|title= Contributions to the relativistic mechanics of continuous media|journal=Gen. Rel. Grav.|volume=25|pages=1225–1266|year=1993|doi=10.1007/BF00759031 (for the journal's "Golden Oldies" section)]

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. [The changing views of what eventually be regarded as black holes can be found in Citation
last=Israel
first=Werner
contribution=Dark stars: the evolution of an idea
editor2-last=Israel
editor2-first=Werner
editor1-last=Hawking
editor1-first=Stephen W.
title=300 Years of Gravitation
publisher=Cambridge University Press
year=1987
pages=199–276
isbn=0-521-37976-8
. Ehlers' thesis is Citation
last=Ehlers
first=Jürgen
title=Konstruktionen und Charakterisierungen von Lösungen der Einsteinschen Gravitationsfeldgleichungen
publisher=University of Hamburg
year=1957
(in German, English translation of title: "Constructions and characterizations of solutions of Einstein's gravitational field equations").
]

Ehlers group

In physics, a duality symmetry exists 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 $o$B, B $o$ E leaves Maxwell's equations invariant. [E.g. Citation|last=Olive|first=D. I.|title=Exact Electromagnetic Duality|journal=Nucl. Phys. B (Proc. Suppl)|volume=45A|year=1996|pages=88–102]

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 $SL\left(2\right)$ 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. [As described in Citation|last=Maison|first=Dieter|contribution=Duality and Hidden Symmetries in Gravitational Theories|editor-last=Schmidt|editor-first=Bernd G.|title=Einstein's Field Equations and Their Physical Implications|year=2006|publisher=Springer|pages=273–323|isbn=3-540-67073-4. For the generalizations, see Citation|last=Geroch|first=R.|title=A method for generating new solutions of Einstein’s ﬁeld equation. I|journal=J. Math. Phys.|volume=12|year=1971|pages=918–924|doi=10.1063/1.1665681; for the applications, Citation|last=Mars|first=Marc|title= Space-time Ehlers group: Transformation law for the Weyl tensor|journal=Class. Quant. Grav.|volume=18|pages=719–738|year=2001|doi= 10.1088/0264-9381/18/4/311.]

Cosmology: Ehlers-Geren-Sachs theorem

The models of modern cosmology are based on the Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes of general relativity. Robertson-Walker universes are perfectly isotropic and homogeneous – but how do we know that this is a good approximative description of our actual universe? While observations of the large-scale distribution of galaxies provides valuable evidence, the most stringent limit comes from another data set: the properties of the cosmic background radiation, and "electromagnetic echo" produced around 400,000 years after the big bang. [For galaxy observations, cf. Citation
last=Peebles
first=P.J.E.
first2=D.N.
last2=Schramm
first3=E.L.
last3=Turner
first4=R.G.
last4=Kron
year=1991
doi=10.1038/352769a0
title=The case for the relativistic hot Big Bang cosmology
journal=Nature
volume=352
pages=769–776
. For a basic description of the cosmic background radiation, cf. chapter 11 in Citation
last=Bergström
first=Lars
first2=Ariel
last2=Goobar
year=2003
title=Cosmology and Particle Astrophysics
edition=2nd
publisher=Wiley & Sons
isbn= 3-540-43128-4
.
]

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. Using the fact that, as measured from Earth, the cosmic microwave background is indeed highly isotropic – the temperature characterizing this thermal radiation varies only by tenth of thousandth of a Kelvin with the direction of observations –, and making the Copernican assumption that Earth does not occupy a privileged cosmic position, this constitutes the strongest available evidence for our own universe's homogeneity and isotropy, and hence for the foundation of current standard cosmological models. Strictly speaking, this conclusion has a potential flaw. While the Ehlers-Geren-Sachs theorem concerns only exactly isotropic measurements, it is known that the background radiation does have minute irregularities. This was addressed by a generalization published in 1995 by W. R. Stoeger, Roy Maartens and George Ellis, which shows that an analogous result holds for observers who measure a nearly isotropic background radiation, and can justly infer to live in a nearly FLRW universe. [See pp. 351ff. in Citation
last1=Hawking
first1=Stephen W.
last2=Ellis
first2=George F. R.
title=The large scale structure of spacetime
publisher=Cambridge University Press
isbn=0-521-09906-4
year=1973
. The original work is Ehlers, J., Geren, P., Sachs, R.K.: Isotropic solutions of Einstein-Liouville equations. J. Math. Phys. 9, 1344 (1968). For the generalization, see Citation|last=Stoeger|first=W. R.|last2=Maartens|first2=R|last3=Ellis|first3=George|author3-link=George Ellis|title=Proving Almost-Homogeneity of the Universe: An Almost Ehlers-Geren-Sachs Theorem|journal=Ap. J.|volume=39|year=2007|pages=1–5|doi=10.1086/175496.
]

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. [Citation
last=Ehlers
first=Jürgen
last2=Pirani
first2=F. A. E.
last3=Schild
first3=Alfred
editor-last=O'Raifeartaigh
editor-first=L.
title=General Relativity
publisher=Clarendon Press
year=1972
page=63
; a summary can be found in Citation
last=Ehlers
first = Jürgen
contribution=Survey of general relativity theory
editor-last=Israel
editor-first=Werner
title=Relativity, Astrophysics and Cosmology
year=1973
publisher=D. Reidel
pages=1–125
isbn=90-277-0369-8
]

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. [See Citation|last=K&ouml;hler|first=Egon|last2=Schattner|first2=Ruprecht|title= Some results on pseudorigid motions|journal=General Relativity and Gravitation|doi=10.1007/BF00756906|volume=10|year=1979|pages=709–716. The original publication is Citation|last=Ehlers|first=Jürgen|last2=Rudolph|first2=Ekkart|title=Dynamics of extended bodies in general relativity center-of-mass description and quasirigidity|journal=General Relativity and Gravitation|doi=10.1007/BF00763547|volume=8|year=1977|pages=197–217.]

Gravitational lensing

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 &mdash; assuming the gravitational field to be small and the deflection angles to be minute &mdash; 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. [Cf. the review Citation|title=Book-Review - Gravitational Lenses|last=Bleyer|first=U.|journal=Astronomische Nachrichten|volume=314|pages=314–315|year=1993|url=http://adsabs.harvard.edu/abs/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 Citation|last=Perlick|first=Volker|title=Book review:Petters, A.O., Levine, H., Wambsganss, J.: Singularity theory and gravitational lensing|journal=Gen. Relativ. Gravit.|year=2005|volume=37|pages=435–436|doi=10.1007/s10714-005-0033-z and Citation|first=Valerio|last=Bozza|title=Book review: Silvia Mollerach, Esteban Roulet: Gravitational Lensing and Microlensing|journal=General Relativity and Gravitation|volume=37|pages=1335–1336|year=2005|doi=10.1007/s10714-005-0117-9.] In the following years, Ehlers continued his research on the propagation of bundles of light in arbitrary spacetimes. [Citation|last=Seitz|first=S.|last2=Schneider|first2=P.|last3=Ehlers|first3=J.|title=Light propagation in arbitrary spacetimes and the gravitational lens approximation|journal=Class. Quantum Grav.|volume=11|pages=2345–2383|year=1994|doi=10.1088/0264-9381/11/9/016,cf. section 3.5 of Citation|title=Annual Report 1994|publisher=Max Planck Institute for Astrophysics|year=1995|url=http://www.mpa-garching.mpg.de/mpa/institute/annual_rep/Jahresbericht_94.ps.gz]

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 $lambda$ 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. [Cf. Citation|last=Ehlers|fist=J.|title=Examples of Newtonian limits of relativistic spacetimes|journal=Classical and Quantum Gravity|year=1997|pages=A119–A126|doi=10.1088/0264-9381/14/1A/010 ; a description can be found on p. 216f. in Citation|last=Blanchet|first=Luc|contribution=Post-Newtonian Gravitational Radiation|editor-last=Schmidt|editor-first=Bernd G.|title=Einstein's Field Equations and Their Physical Implications|year=2006|publisher=Springer|pages=225–271|isbn=3-540-67073-4.]

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 quadrupol 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. [A description that include the historical context can be found in Citation|last=Schutz|first=B. F.|title=Making the Transition from Newton to Einstein: Chandrasekhar’s Work on the Post-Newtonian Approximation and Radiation Reaction|journal=J. Astrophys. Astr.|volume=17|pages= 183–197|url=http://www.ias.ac.in/jarch/jaa/17/183-197.pdf|year=1996|doi=10.1007/BF02702303.The original work is Citation|last=Ehlers|first=J.|last2=Rosenblum|first2=A.|last3=Goldberg|first3=J. N.|last4=Havas|first4=Peter|journal=Astrophys. J.|volume=208|page=L77.]

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. [Citation
last=Buchert
first=Thomas
last2=Ehlers
first2=Jürgen
year=1993
title=Lagrangian theory of gravitational instability of Friedmann-Lemaître cosmologies – second-order approach: an improved model for nonlinear clustering
journal=Mon. Not. R. Astron. Soc.
volume=264
page=375
,Citation
last=Buchert
first=Thomas
last2=Ehlers
first2=Jürgen
year=1997
title=Averaging inhomogeneous Newtonian cosmologies
journal=Astron. Astrophys.
volume=320
pages=1-7
,and Citation
last=Buchert
first=Thomas
last2=Ehlers
first2=Jürgen
year=1997f
title=Newtonian cosmology in Lagrangian formulation: foundations and perturbation theory
journal=General Relativity and Gravitation
volume=29
pages=733–764
. The current status of Buchert's further work is summarized in Citation
last=Buchert
first=Thomas
year=2007
title=Dark Energy from Structure—A Status Report
journal=General Relativity and Gravitation
volume=40
pages=467–527
doi=10.1007/s10714-007-0554-8
id=arxiv|0707.2153
]

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. [E.g. Citation|last=Braun|first=Rüdiger|title=Wo Zeit und Raum aufhören. Der Mitbegründer des Golmer Max-Planck-Instituts für Gravitationsphysik, Jürgen Ehlers, ist unerwartet verstorben|newspaper=Märkische Allgemeine Zeitung|date=May 27, 2008|url=http://www.maerkischeallgemeine.de/cms/beitrag/11216020/60709/Der_Mitbegruender_des_Golmer_Max_Planck_Instituts_fuer.html|year=2008|access-date=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 [http://quantum-history.mpiwg-berlin.mpg.de/ website] .] In particular, he explored Pascual Jordan's seminal contributions to the development of quantum field theory between 1925 and 1928. [Citation|last=Ehlers|first=Jürgen|contribution=Pascual Jordan's Role in the Creation of Quantum Field Theory|editor-last=Ehlers|editor-first=J.|editor2-last=Hoffmann|editor2-first=D.
editor3-last=Renn|editor3-first=Jürgen|title=Pascual Jordan (1902–1980). Mainzer Symposium zum 100. Geburtstag. Preprint Nr. 329|publisher=Max Planck Institute for the History of Science|year=2007|pages=23–35
] During Ehlers' time in Hamburg, there had been a lively exchange between the relativists of the Jordan group and the group of physicist-turned-philosopher Carl Friedrich von Weizsäcker. 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. [Jordan group and Weizsäcker: Citation|last=Breuer|first=Reinhard|title=Universalist, Querdenker, Mystiker: Carl Friedrich von Weizsäcker|journal=Spektrum der Wissenschaft|date=May 2, 2007|year=2007|url=http://www.spektrum.de/artikel/872761&_z=798889 (in German, English translation of title: "Renaissance man, out-of-the-box thinker, mystic: Carl Friedrich von Weizsäcker"). Ehlers' work on the status of scientific knowledge e.g. Citation
last=Ehlers
first=Jürgen
contribution=Physikalische Erkenntnis, dargestellt am Beispiel des Übergangs von Newtons Raumzeit zu Einsteins spezieller Relativitätstheorie
title=Die Kultur moderner Wissenschaft am Beispiel Albert Einstein
editor-last=Balsinger
editor-first=Philipp W.
editor2-first=Rudolf
editor2-last=Kötter
year=2006
pages=1–16
url=http://edoc.mpg.de/345888
(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 Citation|last=Breuer|first=Reinhard|last2=Springer|first2=Michael|title=Die Wahrheit in der Wissenschaft|journal=Spektrum der Wissenschaft|volume=7|year=2001|page=70|url=http://www.spektrum.de/artikel/827796&_z=798889 (in German, English translation of title: "Truth in science").
]

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. [Public lectures: Citation|title=Biennial Report 2004/2005|publisher=Max Planck Institute for Gravitational Physics|year=2006|url=http://www.aei.mpg.de/pdf/illustrationsDocs/biennial2004_05.pdf, 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. Citation|last=Ehlers|first=J.|last2=Fahr|first2=H. J.|title=Urknall oder Ewigkeit|journal=Bild der Wissenschaft|pages=84|year=1994|volume=June] 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. [Citation|title=Biennial Report 2004/2005|publisher=Max Planck Institute for Gravitational Physics|year=2006|url=http://www.aei.mpg.de/pdf/illustrationsDocs/biennial2004_05.pdf lists 11 talks to teachers or in an interdisciplinary setting (p. 147f., p. 154f.). Mathematics and physics: Citation|last=Ehlers|first=Jürgen|title=Mathematik als „Sprache“ der Physik|journal=Praxis der Naturwissenschaften – Physik in der Schule|volume=55|year=2006|url=http://edoc.mpg.de/345898 (in German, English translation of title: "Mathematics as the "language" of physics").]

elected publications

*Citation
last=Ehlers
first = Jürgen
contribution=Survey of general relativity theory
editor-last=Israel
editor-first=Werner
title=Relativity, Astrophysics and Cosmology
year=1973
publisher=D. Reidel
pages=1–125
isbn=90-277-0369-8

*Citation|first=P.|last=Schneider|first2=J.|last2=Ehlers|first3=E. E.|last3=Falco|title=Gravitational lenses|publisher=Springer|year=1992|isbn=3540665064

References

*PND|121317374
* Pages [http://www.aei.mpg.de/ehlers/en/index.html In Memoriam Jürgen Ehlers] at the Albert Einstein Institute

Persondata
NAME=Ehlers, Jürgen
SHORT DESCRIPTION=German physicist, general relativity
DATE OF BIRTH=December 20 1929
PLACE OF BIRTH=Hamburg, Germany
DATE OF DEATH=May 20 2008
PLACE OF DEATH=

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