Claude Barrabès and Peter A. Hogan
OXFORD UNIVERSITY PRESS 2013, 152 PAGES
PRICE (HARDBACK) £60.00 ISBN 978-0-199-68069-6
This book is a research monograph which contains 6 chapters, each of which is intended to serve as a platform from which a beginning graduate student could launch a research project. The expected readership is people who have either completed a taught MSc in General Relativity or have reached this level through self study after completing an introductory book on this subject, e.g. Introduction to Black Hole Physics by Frolov and Zelnikov.
The six chapters cover the following material:
Chapter 1 – is concerned with various kinds of Lorentz transformations, ending with a section on gravitational waves.
Chapter 2 – considers waves, both gravitational and electromagnetic, plane, shock and high frequency. The chapter starts with the approach used in initial courses on general relativity, that of presenting gravitational waves as solutions of the vacuum field equations in linear approximation. It then continues via a sequence of gauge transformations to the metric tensor that is the exact solution of the vacuum field equations. The approach is then to specialise to waves with a Dirac delta function profile.
Chapter 3 – deals with an approach to calculating the equations of motion of various types of particles, e.g. Kerr particles moving in external fields using the appropriate vacuum field equations, that was developed starting in 2008. The chapter ends with a section on spinning test particles. This approach results in avoiding divergent integrals.
Chapter 4 – starts by considering Ozsvath-Robinson-Tozga plane-fronted gravitational waves with a cosmological constant, this eventually leads to gravitational waves appearing in isotropic models as perturbations. Covariant and gauge invariant perturbation theory are covered and used to demonstrate how gravitational waves are introduced into isotropic models.
Chapter 5 – introduces black holes, initially covering basic properties, followed by some classical and quantum aspects of them. The formation of trapped surfaces during gravitational collapse, scattering properties of a high speed Kerr black hole and creation of de Sitter universes inside a black hole are considered.
Chapter 6 – is a short chapter covering black holes in more than 4D space-times. This is usually investigated as part of attempts to unify gravity with the other fundamental forces. The chapter starts with a brief outline of higher dimensional black holes and goes on to consider other aspects including the loop conjecture in D dimensions.
I would recommend this book for people planning a career in General Relativity research or who are considering embarking on a PhD concerning some aspect of this subject.
John Bartlett CMath MIMA
Book review published directly onto IMA website (December 2015)
