- 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_advisor =Pascual Jordan

doctoral_students = Thomas Buchert

known_for =General relativity Mathematical physics

prizes =Max Planck Medal (2002)

religion =

footnotes =**Jürgen Ehlers**(December 29 ,1929 –May 20 ,2008 ) was a Germanphysicist who made notable contributions to the current understanding ofAlbert Einstein 's theory ofgeneral relativity . From graduate and postgraduate work inPascual Jordan 's relativity group atHamburg University , he moved on to various lecturer- and professorships before joining theMax Planck Institute for Astrophysics inMunich as a director. In 1995, he became the founding director of the newly createdMax Planck Institute for Gravitational Physics (Albert Einstein Institute) inPotsdam ,Germany .Ehlers' research focused on the foundations of

general relativity , as well as its applications to various areasastrophysics . In particular, he is notable for his work on the classification ofexact solution s toEinstein's field equations , for theEhlers-Geren-Sachs theorem that justifies the application of simple, general-relativistic model universes to modern cosmology, for aspacetime -oriented description ofgravitational lensing , and for his work on the relationship between models formulated within the framework of general relativity and those ofNewtonian 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 on December 29,1929 in

Hamburg . He attended public schools from 1936 to 1949, and went on to study physics, mathematics, and philosophy atHamburg 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 ofPascual Jordan , with Jordan acting as his thesis advisor. His work on the construction and characterization ofsolution s of theEinstein field equations earned him a doctorate in 1958. [*According to the brief biography appended to Ehlers' dissertation, Citation*] While earlier, the main research of Jordan's group had been dedicated to a scalar-tensor modification of Einstein's theory of

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").general relativity , now known asJordan-Brans-Dicke theory , in which thegravitational 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 includedWolfgang Kundt ,Engelbert Schücking ,Otto Heckmann ,Rainer Sachs , andManfred 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 theUniversity 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 inDallas , and from 1965 to 1971 at theUniversity of Texas in Austin , joiningAlfred 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 inMunich , one of the institutes of Germany's major organization for basic research, theMax Planck Society , as the director of its gravitational theory department. Ehlers' name had been brought into play byLudwig Biermann , the institute's director at the time. Ehlers accepted, and also became an adjunct professor at Munich'sLudwig Maximilian University . In 1991, the institute was split into theMax Planck Institute for Physics and theMax 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 includingAbhay Ashtekar ,Demetrios Christodoulou , andBrandon 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 journalScientific 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 theMax Planck Society dedicated to research on Einstein's theories of gravity. He was successful, and became the founding director of theMax Planck Institute for Gravitational Physics inPotsdam 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 togravitational wave research and headed byBernard 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**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 inMunich (1979). [*Berlin: Citation|url=http://www.bbaw.de/bbaw/Forschung/Forschungsprojekte/akademiegeschichte/en/Mitglieder_Mitarbeiter|access-date=2008-05-27|title=Members/staff, Berliner Akademiegeschichte im 19. und 20. Jahrhundert|publisher=Berlin-Brandenburgische Akademie der Wissenschaften. Mainz: Citation|url=http://www.adwmainz.de/index.php?id=290|access-date=2008-05-27|title=Mitglieder E|publisher=Website of Akademie der Wissenschaften und der Literatur, Mainz (in German, English translation of title: "Members"). Leopoldina: listed as member on Citation|title=Mitgliederverzeichnis|date=August 20, 2007|year=2007|url=http://www.leopoldina-halle.de/mitglied.htm|publisher=Deutsche Akademie der Naturforscher Leopoldina|access-date=2008-05-27 (in German, English translation of title: "Members list"). Bavarian Academy: Listed as corresponding member in Citation|title=Bayerische Akademie der Wissenschaften - Kompetenzen|pages=166|year=2006|publisher=Bayerische Akademie der Wissenschaften|url=http://www.badw.de/publikationen/sonstige/Kompetenzhandbuch_gesamt.pdf|access-date=2008-05-27 (in German, English translation of title: "Bavarian Academy of Sciences - Experts").*] From 1995 to 1998, he served as president of theInternational Society on General Relativity and Gravitation . [*Citation|url=http://grg.maths.qmul.ac.uk/grgsoc/history.html|title=GRG Society History|publisher=Website of the International Society on General Relativity and Gravitation|access-date=2008-05-27.*] He also received the 2002Max Planck Medal of the German Physical Society, the Volta Gold Medal ofPavia University (2005), and the medal of the Faculty of Natural Sciences ofCharles University ,Prague (2007). [*Max Planck Medal: Press release about the 2002 awards, Citation|url=http://www.dpg-physik.de/presse/pressemit/2001/dpg-pm-2001-024.html|title=Physikalische Spitzenleistung|publisher=Deutsche Physikalische Gesellschaft|date=December 17, 2001|year=2001{access-date=2008-05-27 (in German, English translation of title: "Top achievement in physics") and Citation|last=Rogalla|first=Thomas|title=Namen: Prof. Dr. Jürgen Ehlers|url=http://www.berlinonline.de/berliner-zeitung/archiv/.bin/dump.fcgi/2005/0518/wissenschaft/0134/index.html|newspaper=Berliner Zeitung|date=December 28, 2001|year=2001|access-date=2008-05-27 (in German). Volta Medal: Citation|title=Namen: Prof. Dr. Jürgen Ehlers|url=http://www.berlinonline.de/berliner-zeitung/archiv/.bin/dump.fcgi/2005/0518/wissenschaft/0134/index.html|newspaper=Berliner Zeitung|date=May 18, 2005|year=2005|access-date=2008-05-27 (in German) and Citation|title=Medaille für Golmer Forscher|newspaper=Märkische Allgemeine Zeitung|date=May 19, 2005|year=2005 (in German, English translation of title: "Medal for researcher from Golm").*]**Work**Ehlers' research was in the field of

general relativity . In particular, he made important contributions tocosmology , the theory ofgravitational lens es andgravitational 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 solution s ofEinstein'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 fullycovariant theory – its laws are the same, independent of whichcoordinate s are chosen to describe a given situation. One direct consequence is that two apparently differentexact solution s toEinstein'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 solution s toEinstein's field equations , using tools fromdifferential geometry such as thePetrov classification ofWeyl tensor s (that is, those parts of theRiemann tensor describing thecurvature ofspace-time which are not constrained byEinstein's equations ),isometry groups, andconformal transformations. This work also includes the first definition ofpp-waves , a class of especially simplegravitational wave s, as well as their classification. [*A later version of this paper is Citation*] There were also two treatises on

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.gravitational radiation (one withRainer Sachs , one with Manfred Trümper). The work with Sachs studies, among other things, vacuum solutions with specialalgebra ic properties, using the 2-componentspinor 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 byRoy Kerr of theKerr solution , describing a rotatingblack 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=*] The last of these seminal papers dealt with the general-relativistic treatment of the mechanics of continuous media. [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").*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 ofblack 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 itshorizon , in particular that the gravitational field inside cannot bestatic , 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 theelectric field **E**and themagnetic field field**B**in source-freeelectrodynamics , where the replacement**E**$o$ –**B**,**B**$o$**E**leavesMaxwell'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 astationary vacuum spacetime , which mapssolutions 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 $SL(2)$ symmetry which became known as theEhlers group . Further generalizations led to the discovery of the infinite-dimensionalGeroch group (the Geroch group is generated by two non-commutingsubgroup s, one of which is the Ehlers group). These so-called "hidden symmetries" play an important role in theKaluza-Klein reduction of both general relativity and its generalizations, such as eleven-dimensionalsupergravity . 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 anintegrable 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 andhomogeneous – 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 thecosmic background radiation , and "electromagnetic echo" produced around 400,000 years after thebig 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 andRainer 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 fromEarth , the cosmic microwave background is indeed highly isotropic – the temperature characterizing thisthermal radiation varies only by tenth of thousandth of aKelvin with the direction of observations –, and making theCopernican 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 andGeorge 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.

author2-link=George Ellis

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 asevent ,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, thedifferential 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 inradar . 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=90-277-0369-8In 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=Köhler|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 — assuming thegravitational 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. [*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 byElie Cartan ,Kurt Friedrichs and others showed more concretely how a geometrical generalization of Newton's theory of gravity known asNewton-Cartan theory could be understood as a (degenerate) limit ofgeneral 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 simplepoint particle ; in addition, Newtonian versions of interesting exact solutions such as the Friedman-Lemaître models or theGödel 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 thebinary 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 [*] In particular, he explored Pascual Jordan's seminal contributions to the development of*http://quantum-history.mpiwg-berlin.mpg.de/ website*] .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.*] 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

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=23–35Carl 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

publisher=Elsevier/Spektrum Akademie Verlag

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 ofScientific 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 onmathematics 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|editor-last=Börner|editor-first=G.|editor2-last=Ehlers|editor2-first=J.|title=Gravitation|publisher=Spektrum Akademischer Verlag|year=1996|isbn=3-86025-362-X

*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****External links***PND|121317374

* Pages [*http://www.aei.mpg.de/ehlers/en/index.html In Memoriam Jürgen Ehlers*] at theAlbert Einstein Institute Persondata

NAME=Ehlers, Jürgen

SHORT DESCRIPTION=Germanphysicist ,general relativity

DATE OF BIRTH=December 20 1929

PLACE OF BIRTH=Hamburg ,Germany

DATE OF DEATH=May 20 2008

PLACE OF DEATH=

*Wikimedia Foundation.
2010.*

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**Jürgen Ehlers**— ist der Name folgender Personen: Jürgen Ehlers (Physiker) (1929–2008), deutscher Physiker Jürgen Ehlers (Iranist) (* 1930), deutscher Iranist Jürgen Ehlers (Autor) (* 1948), deutscher Geograph und Schriftsteller, Experte für Geologie des… … Deutsch Wikipedia**Jürgen Ehlers**— (29 décembre 1929 – 20 mai 2008) était un physicien allemand, auteur de contributions notoires pour la compréhension de la théorie de la relativité générale d Albert Einstein. Après ces études de premier second cycle dans l équipe de relativité… … Wikipédia en Français**Jürgen Ehlers (Physiker)**— Jürgen Ehlers anlässlich der Verleihung der Medaille der Karls Universität Prag Jürgen Ehlers (* 29. Dezember 1929 in Hamburg; † 20. Mai 2008) war ein deutscher Physiker, der wichtige Beiträge zur einsteinschen Allgemeinen Relativitätstheorie… … Deutsch Wikipedia**Jürgen Ehlers (Autor)**— Jürgen Ehlers Jürgen Ehlers (* 2. Mai 1948 in Hamburg) ist ein deutscher Geograph und Schriftsteller. Einer breiten Öffentlichkeit wurde er durch seine Kriminalromane und erzählungen bekannt. Er ist ein führender deutscher Experte in der Geologie … Deutsch Wikipedia**Jürgen Ehlers (Iranist)**— Jürgen Ehlers im Februar 2011 Jürgen Ehlers (* 28. Mai 1930 in Hamburg) ist ein deutscher Iranist. Er ist in Fachkreisen für seine Arbeiten über das persische Nationalepos, das Šāhnāme, bekannt geworden. Leben Jürgen Ehlers hat in Hamburg die… … Deutsch Wikipedia**Ehlers**— ist der Familienname folgender Personen: Adolf Ehlers (1898–1978), deutscher Politiker (KPD, SPD) Beth Ehlers (* 1968), US amerikanische Schauspielerin Caspar Ehlers (* 1960), deutscher Historiker Claus Ehlers (* 1944), deutscher Politiker (CDU)… … Deutsch Wikipedia**Ehlers (surname)**— Ehlers may refer to the following people with the surnme:* Adolf Ehlers (1898 1978), German politician (KPD, SPD); (de) * Arthur H. Ehlers * Beth Ehlers (born 1968), US actress * Claus Ehlers (born 1944), German politician (CDU); (de) * Dirk… … Wikipedia**Ehlers group**— In mathematical physics, the Ehlers group, named after Jürgen Ehlers, is a finite dimensional transformation group of stationary vacuum spacetimes which maps solutions of Einstein s field equations to other solutions. It has since found a number… … Wikipedia**Jürgen Grube**— (* 1702; † 9. Juli 1776 in Uetersen) war ein deutscher Autor, königlich dänischer Kanzleirat, Regierungs und Obergerichtsadvokat. Leben Er war Sekretär des Uetersener Propstes und Gutsherrn der holsteinischen Güter Jersbek und Stegen Benedikt von … Deutsch Wikipedia**Joachim Ehlers**— (* 31. Mai 1936 in Leipzig) ist ein deutscher Historiker für mittelalterliche Geschichte. Joachim Ehlers wuchs als Sohn eines Landwirts und Wehrmachtsbeamten in seiner Geburtsstadt Leipzig auf. Ehlers machte 1957 das Abitur in Oldenburg und… … Deutsch Wikipedia