Jürgen Ehlers (1929–2008)

Obituary

Jürgen Ehlers (1929–2008)     

Republication of: Exact solutions of the field equations of the general theory of relativity

This is an English translation of a paper by Pascual Jordan, Jürgen Ehlers and Wolfgang Kundt, first published in 1960. The original paper was part 1 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein’s equations found until then. (The other parts of the series will be printed as Golden Oldies in the future.) The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. It is accompanied by an editorial note written by G. F. R. Ellis, and by the biographies of the authors: P. Jordan (written by A. Krasiński) and W. Kundt (written by himself). The biography of J. Ehlers is contained elsewhere in the same issue of GRG, which is devoted to his memory. An editorial note to this paper and a biography can be found in this issue preceding this Golden Oldie and online via doi:. Original paper: Pascual Jordan, Jürgen Ehlers, Wolfgang Kundt, Strenge L?sungen der Feldgleichungen der Allgemeinen Relativit?tstheorie. Akademie der Wissenschaften und der Literatur, Abhandlungen der Mathematisch-naturwissenschaftliche Klasse Nr 2S (1960), pp. 21–105. Reprinted with the kind permission of the Academy of Sciences and Literature, Mainz, and of the authors: Jürgen Ehlers and Wolfgang Kundt. Translated by Anita Ehlers, Anita.Ehlers@t-online.de, and by Manfred Trümper, manfred@truemper.fr, with ample help from Wolfgang Kundt. P. Jordan (Deceased July 31, 1980) J. Ehlers (Deceased May 20, 2008)

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Strong lensing in the Einstein–Straus solution

We analyse strong lensing in the Einstein–Straus solution with positive cosmological constant. Our result confirms Rindler and Ishak’s finding that a positive cosmological constant decreases the bending of light by an isolated spherical mass. In agreement with an analysis by Ishak et al., this decrease is found to be attenuated by a homogeneous mass distribution added around the spherical mass and by a recession of the observer. For concreteness we compare the theory to the light deflection of the lensed quasar SDSS J1004+4112. To the memory of Jürgen Ehlers.     

The Euler–Poisson–Darboux equation for relativists

The Euler–Poisson–Darboux (EPD) equation is the simplest linear hyperbolic equation in two independent variables whose coefficients exhibit singularities, and as such must be of interest as a paradigm to relativists. Sadly it receives scant treatment in the textbooks. The first half of this review is didactic in nature. It discusses in the simplest terms possible the nature of solutions of the EPD equation for the timelike and spacelike singularity cases. Also covered is the Riemann representation of solutions of the characteristic initial value problem, which is hard to find in the literature. The second half examines a few of the possible applications, ranging from explicit computation of the leading terms in the far-field backscatter from predominantly outgoing radiation in a Schwarzschild space–time, to computing explicitly the leading terms in the matter-induced singularities in plane symmetric space–times. There are of course many other applications and the aim of this article is to encourage relativists to investigate this underrated paradigm. To the memory of Jürgen Ehlers whose breadth of knowledge and clarity of exposition were and are exemplary for all of us.     

The Newtonian limit of spacetimes for accelerated particles and black holes

Solutions of vacuum Einstein’s field equations describing uniformly accelerated particles or black holes belong to the class of boost-rotation symmetric spacetimes. They are the only explicit solutions known which represent moving finite objects. Their Newtonian limit is analyzed using the Ehlers frame theory. Generic spacetimes with axial and boost symmetries are first studied from the Newtonian perspective. The results are then illustrated by specific examples such as C-metric, Bonnor–Swaminarayan solutions, self-accelerating “dipole particles”, and generalized boost-rotation symmetric solutions describing freely falling particles in an external field. In contrast to some previous discussions, our results are physically plausible in the sense that the Newtonian limit corresponds to the fields of classical point masses accelerated uniformly in classical mechanics. This corroborates the physical significance of the boost-rotation symmetric spacetimes. Dedicated to the memory of Jürgen Ehlers (29 December 1929 to 20 May 2008).     

A canonical dynamics view of the Newtonian limit of general relativity

The Newtonian limit of general relativity was Jürgen Ehlers favourite model for limit relations between theories of physics. In this contribution, for the case of isolated systems, the Newtonian limit of general relativity will be illuminated from a canonical dynamics point of view. The canonical dynamics approach naturally supplies a post-Newtonian expansion of general relativity.     

Existence of families of spacetimes with a Newtonian limit

Jürgen Ehlers developed frame theory to better understand the relationship between general relativity and Newtonian gravity. Frame theory contains a parameter λ, which can be thought of as 1/c ², where c is the speed of light. By construction, frame theory is equivalent to general relativity for λ > 0, and reduces to Newtonian gravity for λ = 0. Moreover, by setting , frame theory provides a framework to study the Newtonian limit . A number of ideas relating to frame theory that were introduced by Jürgen have subsequently found important applications to the rigorous study of both the Newtonian limit and post-Newtonian expansions. In this article, we review frame theory and discuss, in a non-technical fashion, some of the rigorous results on the Newtonian limit and post-Newtonian expansions that have followed from Jürgen’s work.     

Republication of: The geometry of free fall and light propagation

This is a reprinting of the paper by Jürgen Ehlers, Felix Pirani and Alfred Schild, first published in 1972 in a separate volume containing articles written in hounour of J. L. Synge. The original book is long out of print and almost forgotten by today. The authors present a method of deriving the Lorentzian geometry from compatible conformal and projective structures on a four dimensional manifold. The paper has been selected by the Editors of General Relativity and Gravitation for re-publication in the Golden Oldies series of the journal. This republication is accompanied by an editorial note written by Andrzej Trautman.     

Republication of: The redshift of extragalactic nebulae

This English translation of the paper by F. Zwicky, “Die Rotverschiebung von extragalaktischenNebeln”, Helv. Phys. Acta 6, 110–127 (1933), in which he concludedfrom the results of observations that the amount of non-luminous matter in the Universe must be greaterthan that of luminous matter—thus becoming an early precursor of the dark matter idea, has beenselected for publication in the Golden Oldies series of General Relativity and Gravitation. The paper is accompanied by an editorialnote written by Jürgen Ehlers and by Zwicky’s brief biography compiled by Andrzej Krasiński.     

Jürgen Ehlers—and the fate of the black-hole spacetimes

This article—written in honour of Jürgen Ehlers—consists of two different, though interlocking parts: Sect. 1 describes my 54 years of perpetual experiences and exchanges with him, both science and episodes, whilst Sect. 2 describes 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.     

Schwarzschild black hole as moving puncture in isotropic coordinates

The success of the moving puncture method for the numerical simulation of black hole systems can be partially explained by the properties of stationary solutions of the 1 + log coordinate condition. We compute stationary 1 + log slices of the Schwarzschild spacetime in isotropic coordinates in order to investigate the coordinate singularity that the numerical methods have to handle at the puncture. We present an alternative integration method to obtain isotropic coordinates that simplifies numerical integration and that gives direct access to a local expansion in the isotropic radius near the puncture. Numerical results have shown that certain quantities are well approximated by a function linear in the isotropic radius near the puncture, while here we show that in some cases the isotropic radius appears with an exponent that is close to but unequal to one. This paper is dedicated to the memory of Jürgen Ehlers. I have known JE for a number of years, in particular during his time as founding director of the Albert Einstein Institute in Potsdam. JE was the mentor of my habilitation thesis in 1996, and I am deeply thankful for many insightful discussions. JE combined great breadth and physical intuition with sharp analytical thought. His example inspired me to look beyond the numerical methods and results of numerical relativity to the analytic foundations. For example, while at the AEI, S. Brandt and I introduced “puncture initial data” for the numerical construction of general multiple black hole spacetimes [3]. While the puncture construction starts with an analytic trick of the sort that numerical relativists may devise, it is fair to say that the keen interest in analytical relativity created by JE at the AEI induced us to push our analysis one step further. As a result [3] connects to [26] for an existence and uniqueness proof for such black hole initial data, using weighted Sobolev spaces (see also [4–6]). The present work and its predecessors [9–12] represent an example where numerical experiments led to the discovery of an analytic solution for the 1 + log gauge for the Schwarzschild solution, and the present result, although modest, is of the type which I believe JE would have appreciated.     

A Quantum-Chemical Investigation of the Geometry and NMR Chemical Shifts of Bilirubin

A computational investigation using density-functional-theory methods has been performed concerning the structure and nuclear magnetic resonance (NMR) chemical shifts of bilirubin with a special emphasis on the hydrogen bonds. Solid-state effects on the NMR spectra are investigated by considering a trimeric model derived from the available X-ray structure. Satisfactory agreement between theory and experiment is found with ring-current effects playing only a minor role for the interpretation of the solid-state NMR spectra. Authors' address: Jürgen Gauss, Institut für Physikalische Chemie, Universit?t Mainz, 55099 Mainz, Germany     

The truth in science

Are natural scientists gaining an ever more complete picture of reality through their objective insights, or are the truths of the natural sciences no more than consensuses that change with time? The astrophysicist Jürgen Ehlers and the social scientist Rudolf Stichweh talk to Spektrum.     

Neutron experiments with cryogenic methane hydrate and mesitylene moderators

In this article we describe the experimental results of a methane hydrate moderator as well as as mesitylene moderator operated at a temperature around 20K at the JESSICA (Jülich Experimental Spallation Target Set-up In COSY Area) experiment at the Jülich cooler synchrotron COSY. For the first time the cold neutron spectrum of a methane hydrate moderator was experimentally investigated. A comparison with a solid methane and an ice moderator atT = 20 K will be shown. MCNPX simulations with new developedS(α,β) scattering kernels will be compared with experimental data. The applicability of mesitylene and methane hydrate as cold moderators at spallation neutron sources will be discussed.     

Physics with the new WASA-at-COSY facility

The Wide Angle Shower Apparatus (WASA), previously operated at Uppsala, Sweden, is now installed at the COSY accelerator at Jülich Forschungszentrum, Germany. The main goal of the WASA-at-COSY collaboration is to study symmetry violations in hadronic reactions focusing on η and η′ decays. The Nuclear Physics Institute at Jülich Forschungszentrum and Department of Physics at IIT Bombay are collaborating to understand QCD at intermediate distance scales using the proton beam from the COSY accelerator with proton and deuteron targets. In this paper, we present the preliminary analysis on three different channels being investigated jointly by the two groups.     

Exploding dissipative solitons in the cubic-quintic complex Ginzburg-Landau equation in one and two spatial dimensions

We review the work on exploding dissipative solitons in one and two spatial dimensions. Features covered include: the transition from modulated to exploding dissipative solitons, the analogue of the Ruelle-Takens scenario for dissipative solitons, inducing exploding dissipative solitons by noise, two classes of exploding dissipative solitons in two spatial dimensions, diffusing asymmetric exploding dissipative solitons as a model for a two-dimensional extended chaotic system. As a perspective we outline the interaction of exploding dissipative solitons with quasi one-dimensional dissipative solitons, breathing quasi one-dimensional solutions and their possible connection with experimental results on convection, and the occurence of exploding dissipative solitons in reaction-diffusion systems. It is a great pleasure to dedicate this work to our long-time friend Hans (Prof. Dr. Hans Jürgen Herrmann) on the occasion of his 60th birthday.     

Fourth ANKA and KNMF User Meeting 2012

On October 10–11, 2012, the ANKA synchrotron radiation facility and the Karlsruhe NanoMicro Facility (KNMF), both user research facilities at the Karlsruhe Institute of Technology (KIT) in Germany, hosted their fourth joint annual user meeting at the Ettlingen Castle. In the extraordinary ambiance of the baroque palace, the ANKA and KNMF directorates (represented by Clemens Heske and Jürgen Mohr, respectively) welcomed almost 200 participants representing universities, research facilities, and companies from 10 different countries. The meeting was kicked off by KIT Chief Science Officer Volker Saile, who emphasized the positive developments and increase in user numbers at both facilities.     

Editorial

More than 30 years of scientific endeavor have brought us from programming simple models to impressive simulations of dynamic systems. Lattice models like Potts, percolation, fuse, fiber bundle, and growth models, just to name a few, are the prototypes or godfathers of statistical mechanics. With the availability of more powerful tools it became possible to develop these models and apply them on complex topologies, finding important practical applications in socio-technological systems (e.g., opinion dynamics, traffic, communication networks) and to engineering problems (e.g., fracture phenomena, mass transport). In parallel, particle models evolved from a hand full of interacting discs to three dimensional multibillion particle simulations that successfully describe interesting fracture phenomena, granular flow, and even fluid flow for engineering applications. Prof. Dr. Hans Jürgen Herrmann has dedicated his professional life to this journey.     

Fractional Pais–Uhlenbeck Oscillator

In this paper we study the fractional Lagrangian of Pais–Uhlenbeck oscillator. We obtained the fractional Euler–Lagrangian equation of the system and then we studied the obtained Euler–Lagrangian equation numerically. The numerical study is based on the so-called Grünwald–Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grünwald–Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman–Liouville fractional derivative is equivalent to the Grünwald–Letnikov derivative for a wide class of the functions.     

Many-body calculations for the relaxed (110) surface of GaAs

Quantum Monte Carlo methods are a stochastic approach to directly tackle the manybody problem in solids. They have proven to describe virutually exactly the ground state of correlated bulk systems, like the homogeneous electron gas or solids of C, Ge, Si and GaAs. Especially Variational quantum Monte Carlo calculations using nonlocal ab initio pseudopotentials offer a way to study systematically many-body effects at solid surfaces, safely founded on the variational principle “the lower the energy, the better the wave function”. Here we report on first attempts for the relaxed (110) surface of GaAs, serving as a prototype of semiconductor surfaces. A finite layer geometry is chosen as the boundary condition of the multidimensional stochastic integration scheme. The exact many-body Hamiltonian is cast in a form allowing for rapid evaluation. New parameters in the correlated trial wave function increase the variational freedom necessary to take into account the influence of the surface. Their physical meaning and their statistical significance are discussed in detail. Presented at the VIII-th Symposium on Surface Physics, Třešt’ Castle, Czech Republic, June 28 – July 2, 1999. This work was supported by the Deutsche Forschungsgemeinschaft under Grant No. Scha 360/17-1. Our calculations were performed on the Cray-T3E at the Zentralinstitut für Angewandte Mathematik, Forschungszentrum Jülich, and on the Cray-T3E at the Konrad-Zuse-Zentrum für Informationstechnik, Berlin.