General Relativity and Gravitation (2011) DOI 10.1007/s10714-009-0815-9 RESEARCHARTICLE Wolfgang Kundt Jurgen¨ Ehlers—and the fate of the black-hole spacetimes Received: 16 April 2009 / Accepted: 26 April 2009 c Springer Science+Business Media, LLC 2009 Abstract This article—written in honour of Jurgen¨ Ehlers—consists of two dif- ferent, though interlocking parts: Sect. 1 describes my 54 years of perpetual ex- periences and exchanges with him, both science and episodes, whilst Sect. 2 de- scribes the history of astrophysical black holes, which evolved during the same epoque though largely independently, with its activity centers in other places of the globe, and has by no means terminated. Keywords Ju,¨ rgen EhlersBlack holes, Sgr A* 1 Jurgen¨ Ehlers: our 54 years of close interaction Jurgen¨ Ehlers and I both studied physics and mathematics at Hamburg University. My studies began with the summer ‘Semester’ of 1950, Jurgen’s¨ 1 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 personality of Pascual Jordan, and jointly started weekly seminar work with him. Soon we were joined by Engelbert Schucking,¨ and soon again, Pascual Jordan guided our collaboration, both mentally, and financially. The Hamburg group in General Relativity had been founded. Jurgen,¨ Engelbert, myself, and ‘der Meister’ took turns as weekly seminar speakers. Initially, Jordan’s contributions aimed at improving the second edition of his book ‘Schwerkraft und Weltall’. Jurgen’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 station.did not show My own up at contributions all, whilst absorbing were often this somewhat stuff, possibly premature, in a bar introducing near the train new problems to the group in order to receive feedback, and to profit particularly from W. Kundt Argelander Institut fur¨ Astronomie der Universitat¨ Bonn 53121 53121 Bonn, Ger- many [email protected] 2 W. Kundt Jurgen’s¨ suggestions for deepened understanding. On 4 June 1955, Jurgen¨ 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 during the early 1960s, 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 us gain a certain group knowledge. But there was enough time left for continued learning, and for approaching new prob- lems. We tried to get deeper insights into the different known classes of exact solutions of Einstein’s field equations, their invariant properties, and global con- tinuations. Besides, Jurgen¨ improved his—and our—understanding of relativistic thermodynamics, electromagnetism within GR, and relativistic statistical mechan- ics. 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 stationary cosmological model (with a non-vanishing cosmological constant Λ), in which suitably accelerated observers can travel into their own past. In 1957, our work received a forceful boost by Felix Pirani’s physical evaluation of Petrov’s 1954 algebraic classification 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 valuable tool for analytic evaluations, in particular of (strong) gravitational-wave fields, but also for other classes of ‘al- gebraically 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 solu- tion of the (local) ‘equivalence problem’—later also called ‘isometry problem’— of two given spacetimes, and from results on algebraic invariants by Weitzenbock¨ (1923), Eisenhart (1927, 1933, 1935, 1949), Thomas (1934), Weyl (1939), Cheval- ley (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 complementar- ity’ (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 symmetry 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 [11] and 1962 [5] joint publications with Jurgen¨ listed in the references, though only par- tially highlighted as theorems. Jurgen¨ had done the proof-reading at Hamburg whilst I was in Syracuse (NY)—working in Peter Bergmann’s group for a bit over a year—at an epoch with only snail-mail correspondence. Jurgen¨ 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 Jurgen¨ Ehlers—and the fate of the black-hole spacetimes 3 type of their Riemann tensor, for which the complete system of rational scalar invariants (formed from their metric and Riemann tensor and its covariant deriva- tives) 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 formu- lated the theorems as conjectures, or should we have relegated them to the text? Jurgen’s¨ honest mind preferred the latter. The years 1959–1962 were brainstormy ones for us. The Petrov–Pirani insight had likewise reached ‘relativists’ like Ivor Robinson, who had shown me how to integrate the gravitational field equations analytically, in suitable coordinate gauges, and Andrzej Trautman, Hermann Bondi, Ray Sachs, Roger Penrose, and Ted Newman, among others, who showed us how to analyse the far-field behaviour of radiating sources. For me in particular waited the class of plane-fronted gravi- tational waves, plus its subclass with parallel rays—called ‘pp waves’ for short— which turned out to be extremely instructive: the plane-fronted gravitational 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 invari- ants, as already mentioned 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, Jurgen’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. Jurgen¨ 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 sixty-fifth anniversary was celebrated (in Ham- burg) in October 1967. In all these years, our relativity group was kept alive by new (younger) members, like Manfred Trumper,¨ Bernd Schmidt, Wolf Beiglbock,¨ Klaus Bichteler, Volker Enß, Michael Streubel, Eva Ruhnau, Hans-Jurgen¨ Seifert, Henning Mueller zum Hagen, Hans Seiler, and a few more. We met at international conferences, like the Texas Symposia on Relativistic Astrophysics (introduced by Ivor Robinson, Alfred Schild, and Engelbert Schucking),¨ 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 Jurgen¨ and myself: we partcipated actively in a weekly seminar on the selected book on QED by Jauch and Rohrlich, jointly with Hans-Jurgen¨ Borchers, Hans Joos, Werner Theis, Klaus Helmers, Peter Stichel, Georg Sußmann,¨ and Bert Schroer, because we wanted to learn how to quantise the gravitational field. (Today I think it must not be quantised (2007 [21]), 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 Jurgen¨ was the speaker of the day, and was cautioned by Helmers about an inconsistency of his statement (on the 4 W. Kundt supposedly unitary correspondences between interacting and free fields): Jurgen¨ 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 correspon- dence was mathematically exact.