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Juergen Ehlers-And the Fate of the Black-Hole Spacetimes Noname manuscript No. (will be inserted by the editor) Jurgen¨ Ehlers - and the Fate of the Black-Hole Spacetimes Wolfgang Kundt the date of receipt and acceptance should be inserted later Abstract This article – written in honour of J¨urgen Ehlers – consists of two different, though interlocking parts: Section 1 describes my 54 years of perpetual experiences and exchanges with him, both science and episodes, whilst section 2 describes the history of astrophysical black holes, which evolved during the same epoque though largely indepen- dently, with its activity centers in other places of the globe, and has by no means terminated. 1 J¨urgen Ehlers: our 54 years of close Interaction J¨urgen Ehlers and I both studied physics and mathematics at Hamburg University. My stud- ies began with the summer ‘Semester’ of 1950, J¨urgen’s one year earlier; (he was born on 29 November 1929, & 18 months before me). When we scientifically matured to terminate our standard education – in the fall of 1953, I think – we were both attracted by the person- ality of Pascual Jordan, and jointly started weekly seminar work with him. Soon we were joined by Engelbert Sch¨ucking, and soon again, Pascual Jordan guided our collaboration, both mentally, and financially. The Hamburg group in General Relativity had been founded. J¨urgen, Engelbert, myself, and ‘der Meister’ took turns as weekly seminar speakers. Initially, Jordan’s contributions aimed at improving the second edition of his book ‘Schw- erkraft und Weltall’. J¨urgen’s contributions educated us primarily on other people’s work: they helped us understand it thoroughly. And Engelbert excited us with brand new stuff which had somehow entered his mind; unless he did not show up at all, whilst absorbing this stuff, possibly in a bar near the train station. My own contributions were often some- what premature, introducing new problems to the group in order to receive feedback, and to profit particularly from J¨urgen’s suggestions for deepened understanding. On 4 June 1955, arXiv:0905.1028v1 [astro-ph.HE] 7 May 2009 J¨urgen met (his later wife) Anita, on a large faculty dance in the (decorated) mensa of the university which I had organised. Our scientific work was done largely independently, mainly at home, except when an ‘airforce report’ had to be written, for Jordan’s contract with the U.S. army, or when dur- ing the early 60s, survey papers had to be composed for the ‘Akademie der Wissenschaften und der Literatur in Mainz’, of which Jordan was a member. Such joint publications helped W. Kundt Argelander Institut f¨ur Astronomie der Universit¨at Bonn 2 us gain a certain group knowledge. But there was enough time left for continued learning, and for approaching new problems. We tried to get deeper insights into the different known classes of exact solutions of Einstein’s field equations, their invariant properties, and global continuations. Besides, J¨urgen improved his – and our – understanding of relativistic ther- modynamics, electromagnetism within GR, and relativistic statistical mechanics. And we searched for reliable ways to decide when two given line elements could be transformed into each other, by a suitable change of coordinates. This program began with a discussion of Kurt Goedel’s (1949) homogeneous and sta- tionary cosmological model (with a non-vanishing cosmological constant Λ), in which suit- ably accelerated observers can travel into their own past. In 1957, our work received a forceful boost by Felix Pirani’s physical evaluation of A.S. Petrov’s 1954 algebraic clas- sification of the Weyl tensor for normal-hyperbolic metrical spaces, i.e. of the traceless Riemann tensor, as for vacuum spacetimes. Petrov’s classification turned out to be a valu- able tool for analytic evaluations, in particular of (strong) gravitational-wave fields, but also for other classes of ‘algebraically degenerate’ spacetimes in which the eigen values of the Weyl tensor tend to yield invariant coordinates. Other tools for characterisation came from Elie Cartan’s (1946) basic work on Riemannian spacetimes, in particular a solution of the (local) ‘equivalence problem’ – later also called ‘isometry problem’ – of two given space- times, and from results on algebraic invariants by Weitzenb¨ock (1923), Eisenhart (1927, 1933, 1935, 1949), Thomas (1934), Weyl (1939), Chevalley (1946), and Ruse (1946), as well as by Blaschke (1950), Taub (1951), Schouten (1954), Boerner (1955), Komar (1955), Lichnerowicz (1955), Yano (1955), and Trautman (1958). We thus arrived in addition at the ‘theorem of complementarity’ (of scalar differential invariants and group trajectories) which states that a possible r-dim group of isometries of a given n-dim spacetime Vn – with q-dim trajectories, q := r-s – contains complementary information about its geometry in the sense that one can find n-q independent scalar invariants which complete a system of q symme- try coordinates to a full (local) n-dim coordinate system of Vn ; where s = r-q denotes the dimension of the isotropy group of a generic point. Homogeneous subspaces are invariantly embedded. These two theorems – on constructing (or not) an isometry between two given Vn with or without homogeneous subspaces – were contained in my 1958 ph.d. thesis (including proof sketches), and can be found again in my 1960 and 1962 joint publications with J¨urgen listed in the references, though only partially highlighted as theorems. J¨urgen had done the proof-reading at Hamburg whilst I was in Syracuse (N.Y.) – working in Peter Bergmann’s group for a bit over a year – at an epoch with only snail-mail correspondence. J¨urgen knew that I had discovered an oversight (in my first writeup, and in other people’s proofs) which applies only in the rare case of spaces with an indefinite metric, and of a special type of their Riemann tensor, for which the complete system of rational scalar invariants (formed from their metric and Riemann tensor and its covariant derivatives) gets functionally dependent, so that one has to take recourse to new methods of constructing scalar invariants, involving differential calculus. One such nasty special case turned up in the subclass of the pp waves (see below), with higher (than the usual 2-dim) symmetry, and served as a counter example to published results even though it was fairly clear how to repair them. Should we have for- mulated the theorems as conjectures, or should we have relegated them to the text? J¨urgen’s honest mind preferred the latter. The years 1959-1962 were brainstormy ones for us. The Petrov-Pirani insight had like- wise reached ‘relativists’ like Ivor Robinson, who had shown me how to integrate the grav- itational field equations analytically, in suitable coordinate gauges, and Andrzej Trautman, Hermann Bondi, Ray Sachs, Roger Penrose, and Ted Newman, among others, who showed 3 us how to analyse the far-field behaviour of radiating sources. For me in particular waited the class of plane-fronted gravitational waves, plus its subclass with parallel rays – called ‘pp waves’ for short – which turned out to be extremely instructive: The plane-fronted grav- itational waves show strong resemblances to their electromagnetic analogs in flat spacetime, but are richer as a class. They are among Einstein’s vacuum fields with the largest groups of isometries, and with the most extreme behaviour of their scalar invariants, as already men- tioned above. Their action on clouds of test particles could be elucidated, and they could be shown to be geodetically complete. Clearly, during the years of their analysis, J¨urgen’s interest and advice meant a great challenge to me. But like every human activity, Hamburg’s relativity group did not enjoy eternal life: The year 1962 saw me build my house in Hamburg-Hoheneichen, and move into it in November that same year. J¨urgen and Anita spent several years abroad, between 1961 and 1971, in Syracuse, Dallas, and Austin (Texas), and Ulrike and I spent our honeymoon year 1966/7 in Pittsburgh (Pa), as guests of Ted Newman and his family. Pascual Jordan’s 65th anniversary was celebrated (in Hamburg) in October 1967. In all these years, our relativity group was kept alive by new (younger) members, like Manfred Tr¨umper, Bernd Schmidt, Wolf Bei- glb¨ock, Klaus Bichteler, Volker Enß, Michael Streubel, Eva Ruhnau, Hans-J¨urgen Seifert, Henning Mueller zum Hagen, Hans Seiler, and a few more. We met at international confer- ences, like the Texas Symposia on Relativistic Astrophysics (introduced by Ivor Robinson, Alfred Schild, and Engelbert Sch¨ucking), the Varenna Schools (on lake Como), the Royal Society Meetings in London, and the Marcel Grossmann Meetings (organised by Remo Ruffini, beginning at Trieste). There were frequent, lively international cooperations. There was another intense collaboration during the early 60s, of J¨urgen and myself: we partcipated actively in a weekly seminar on the selected book on QED by Jauch & Rohrlich, jointly with Hans-J¨urgen Borchers, Hans Joos, Werner Theis, Klaus Helmers, Peter Stichel, Georg S¨ußmann, and Bert Schroer, because we wanted to learn how to quantise the gravita- tional field. (Today I think it must not be quantised (2007), because there are no observable effects of quantised gravity: only the equations of state require quantised treatment). I still remember the scene – as though it happened yesterday – when J¨urgen was the speaker of the day, and was cautioned by Helmers about an inconsistency of his statement (on the supposedly unitary correspondences between interacting and free fields): J¨urgen understood immediately, was upset, and threw the library copy of J & R on the desk of our seminar room in disgust, because the formal elegance of the book’s presentation had fooled him, had made him believe that the offered correspondence was mathematically exact.
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