**Reviews of “General relativity, cosmology and astrophysics. Perspectives 100 years after Einstein’s stay in Prague” and “Relativity and gravitation. 100 years after Einstein in Prague”, edited by Jiří Bičák and Tomáš Ledvinka.**

The two volumes under review document the conference held June 25-29, 2012 at Charles University in Prague to commemorate the 100th anniversary of the productive time Einstein spent in Prague, during which he arrived at the principle of equivalence and also formulated other physical principles, summarized in his 1912 paper [1]. This was a crucial step in the development of general relativity, and Einstein devoted the following years to developing its mathematical formulation, finally arriving at the 1915 theory of general relativity, the centennary of which is now celebrated through many events all over the world.

Coincidentally, the 2012 Prague conference also marked the 70th anniversary of the birth of Jiří Bičák, one of the leading European relativists. He was one of the organizers of the conference and is, together with Tomáš Ledvinka, one of the editors of the current volume. The taste and style, as well as the careful attention to detail of both editors, is reflected in the beautifully produced proceedings volumes. As a participant in the conference I can also remark that the same taste and attention to detail was evident in the impeccably organized and enjoyable conference.

In addition to the two book volumes documenting the conference, there is a website which contains abstracts of most talks and posters presented at the conference, as well as video of all plenary talks.

**General Relativity and Gravitation. Perspectives 100 years after Einstein’s stay in Prague**

This volume consists of invited papers based on the plenary talks given in the conference, with a very useful introduction by the editors, giving a capsule review of each plenary talk. The conference was opened by talks of Julian Barbour and Jiří Bičák putting Einstein’s work in Prague in a larger context, and the papers documenting these are also placed first in the volume. Among the great physicists who preceded Einstein in Prague were Kepler and Mach. The paper by Barbour appropriately gives a “Machian” point of view on the development of Kepler ideas on the dynamics of planetary motion, while the paper by Bičák gives an interesting overview of not only of Einstein’s work in Prague, but also of his cultural milieu there, as well as some of the Czech reaction to Einstein’s ideas.

Following these broad historical and philosophical discussions, the volume under review moves across the landscape of modern gravitational physics, from classical GR through quantum gravity and numerical relativity. The section on classical GR opens with an article by Donato Bini laying the foundations of the theory of measurements in general relativity. In the next article, Gary Gibbons gives a wide ranging overview of the role of GR in other parts of physics and this deserves particular mention. One of the topics Gibbons mentions is the role of ideas and techniques originally developed in the context of general relativity to e.g. invisibility cloaks, metamaterials and the analysis of the properties of graphene. Several of the articles in the section are related to black hole physics and gravitational waves, including those by Thibault Damour on the effective one-body formalism, and by Leor Barack on gravitational self-force. <!–Notes ACF

–>The next article by Gerhard Schäfer, which deals with closely related topics, gives a Hamiltonian treatment of the problem of motion, and includes a discussion of recent work on the interaction of spinning black holes. The section also contains a survey by Bob Wald of his work with Stefan Hollands on the relation between the laws of black hole mechanics and the stability properties of black holes. The higher dimensional generalization of the structure that gives rise to the Carter constant for geodesics in the Kerr spacetime, and the related integrability and separability properties for field equations, has been the subject of intense study over the last few years. Many contributions have been made by Valeri P. Frolov and his collaborators, and in his paper in this volume, Frolov gives a useful and readable introduction to these results, focussing on the notion of principal conformal Killing-Yano tensor. Also in this section are papers by Marc Mars on geometric inequalities related to black holes, by Gernot Neugebauer and Jörg Hennig giving a proof of non-existence of stationary black-hole binaries, and by Harvey Reall on higher dimensional black holes.

The section on classical GR is followed by a collection of papers on cosmology and quantum gravity. The papers in this section range from an overview of mathematical results on cosmological models and their relation to the cosmological principle by the author of this review, to a thougthful discussion by Hermann Nicolai of the fundamental problems of quantum gravity from the point of view of particle physics. Nicolai takes advantage of the color printing of the volume by including Brueghel’s painting of the tower of Babel as a perhaps appropriate illustration of the current state of this field. In this section are also three papers relating to the very early universe. These include a paper by Abhay Ashtekar on applications of loop quantum gravity in the very early universe, by Daniel Sudarsky on quantum aspects of inflation, and by Misao Sasaki on the evolution of perturbations in inflationary models with a particular emphasis on non-Gaussianity.

The final section in this volume collects papers on numerical relativity and relativistic astrophysics. The field of numerical relativity is perhaps slightly under-represented in this volume, since only the paper by Luciano Rezzolla has numerical relativity as its main theme (although a paper by Piotr Bizon and Andrezej Rostworowski in the section on classical GR discusses numerical work on the turbulent instability of AdS). The paper by Rezzolla gives an overview of astrophysical applications of numerical relativity by discussing three examples which provide nice illustrations of the interaction of analytical methods and numerical simulations. A review on instabilities of rotating stars is provided in the paper by John Friedman and Nicolas Stergioulas. There are several papers on gravitational waves, including a survey by Bernard Schutz of the state of the art of gravitational wave detectors, including the planned space based detector eLisa, which is also the topic of a separate paper by Gerhard Heinzel and Karsten Danzmann. The best evidence that we have for emission of gravitational waves, until the gravitational wave observatories reach the required sensitivity, is provided by the binary pulsar. This and other aspects of pulsars is discussed in the paper by Michael Kramer. The section, and the volume, closes with two papers exploring highly energetic phenomena associated with rapidly spinning black holes. These are by Marek Abramowicz on the astrophysical signatures of black holes, and by Ramesh Narayan with Jeffrey E. McClintock and Alexander Tchekhovskoy on relativistic jets.

This excellently produced volume contains a collection of papers which provide a broad overview of ongoing research in general relativity and astrophysics. There have been several major such collections around the centennary of Einstein’s birth which are of lasting value, and it is certain that current centennary of general relativity will see several more volumes. The volume under review will compare well to any of these, and I am confident that both established researchers and students will find both enjoyment and enlightement by studying its contents.

**General Relativity and Gravitation. 100 years after Einstein in Prague**

This volume is a companion to the one reviewed above, also edited by Jiří Bičák and Tomáš Ledvinka. It is the proceedings volume of the 2012 Prague conference, collecting papers based on talks and posters presented in the afternoon sessions. The short papers (numbering more than 80) in this volume represent the majority of the talks presented in these sessions and cover essentially the same range of topics as the plenary talks, but are mostly more focussed and relate directly to recent and ongoing research.

The book is divided into four parts, with talks and posters on classical general relativity, cosmology and relativistic astrophysics, and on quantum fields and quantum gravity. Each section contains papers based on talks, followed by papers based on posters. The high quality of the conference is confirmed by the fact that a number of interesting papers are among those based on posters.

Leafing through the volume one encounters also here a couple of nice papers with a historical flavour that are well worth reading. One is by Domenico Giulini who appropriately enough reviews Einstein’s 1912 “Prague” theory of gravity from a modern perspective, and bringing to light many interesting aspects which deserve further study. Another is by Herbert Pfister and gives an overview of gravitomagnetism. A related topic appears in the paper by Donald Lynden-Bell and Joseph Katz who use the gravitomagnetic form of the Einstein equations to construct solutions of Einstein’s equations which contain analogs of solenoids.

There are several interesting papers exploring the geometry of higher dimensional spacetimes. There has been a lot of work on solutions of the higher dimensional Einstein equations motivated in part by considerations in supergravity and string theory. However, the subject has an intrinsic beauty which makes it well worth studying on for its own sake. Among the contributions here, one finds a paper by Naresh Dadhich on Lovelock gravity, by Hervik et al. on electric and magnetic Weyl tensors, and on the Goldberg-Sachs theorem by Ortaggio et al. There are a number of papers on cosmology, including inhomogeneities and the averaging problem, as well as a thoughtful look at the flatness problem in cosmology by Phillip Helbig. Among the more mathematical papers, the paper by Vincent Moncrief and Oliver Rinne on the evolution of the Einstein equations at future null infinity is worth mentioning. This discusses some aspects of analytical and numerical work utilizing a conformal rescaling to bring null infinity (i.e. the location where outgoing radiation such as gravitational can be observed and analyzed) to a finite coordinate location.

The high quality colour printing of the volume is put to good use in several papers on chaos for particle orbits around black holes and other compact objects. As the topic is a local specialty, it is not surprising to find several local scientists among the authors, including Petra Suková and Oldřich Semerák. Their paper discusses geodesic chaos in perturbed black hole fields and is illustrated with many fascinating pictures, as is the paper of Kopáček et al. on a related topic.

To mention just one paper among those on quantum gravity and quantum field theory, I will focus on the paper by Fewster et al. This deals with the probability distributions for quantum stress tensors, i.e. tensors defined by averaging stress tensors defined in terms of quantum fields. This gives rise to energy densities which are not strictly non-negative as one would expect from classical matter, but there quantum energy inequalities which limit the amount of negative energy. The paper by Fewster et al. gives closed form expressions for the case of two-dimensional spacetimes, and estimates for the 4-dimensional case.

It is possible here only to mention a few highlights of this rich proceedings volume. Browsing through the volume is a pleasant and rewarding experience and brings back happy memories of the enjoyable conference at Prague in 2012.

References

[1] A. Einstein. Relativität und Gravitation. Erwiderung auf eine Bemerkung von M.

Abraham. Annalen der Physik, 343:1059–1064, 1912.

**General relativity, cosmology and astrophysics. Perspectives 100 years after Einstein’s stay in Prague**

edited by Jiří Bičák and Tomáš Ledvinka

Springer

535 pages | Hardback

978-3-319-06348-5

Published: 2014

Also available as: eBook

**Price: £99.00**

**Relativity and gravitation. 100 years after Einstein in Prague**

edited by Jiří Bičák and Tomáš Ledvinka

Springer

590 pages | Hardback

978-3-319-06761-2

Published: 2014

Also available as: eBook

**Price: £126.00**

This work is licensed under a Creative Commons Attribution 3.0 Unported License.