Black Holes in General Relativity

As a prelude to our study of quantum black holes, in this chapter we briefly review some of the key features of black holes in general relativity. We focus on specific examples of black hole metrics in four and higher space-time dimensions, which will be

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Xavier Calmet · Bernard Carr Elizabeth Winstanley

Quantum Black Holes

SpringerBriefs in Physics

Series editors Egor Babaev, Massachusetts, USA Malcolm Bremer, Bristol, UK Xavier Calmet, Brighton, UK Francesca Di Lodovico, London, UK Maarten Hoogerland, Auckland, New Zealand Eric Le Ru, Wellington, New Zealand Hans-Joachim Lewerenz, Pasadena CA, USA James Overduin, Towson, USA Vesselin Petkov, Montreal, Canada Charles H.-T. Wang, Aberdeen, UK Andrew Whitaker, Belfast, UK

For further volumes: http://www.springer.com/series/8902

Xavier Calmet Bernard Carr Elizabeth Winstanley •

Quantum Black Holes

123

Xavier Calmet Department of Physics and Astronomy University of Sussex Brighton UK

Elizabeth Winstanley School of Mathematics and Statistics University of Sheffield Sheffield UK

Bernard Carr Department of Physics and Astronomy Queen Mary University of London London UK

ISSN 2191-5423 ISBN 978-3-642-38938-2 DOI 10.1007/978-3-642-38939-9

ISSN 2191-5431 (electronic) ISBN 978-3-642-38939-9 (eBook)

Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2013943713  The Author(s) 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

Preface

This Springer Brief emerged from meetings of Working Group 1 (WG1) of the European Cooperation