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Xavier Calmet Editor Quantum Aspects of Black Holes Fundamental Theories of Physics Fundamental Theories of Physics 178 Xavier Calmet Editor Quantum Aspects of Black Holes Fundamental Theories of Physics Volume 178 Series editors Henk van Beijeren Philippe Blanchard Paul Busch Bob Coecke Dennis Dieks Detlef Dürr Roman Frigg Christopher Fuchs Giancarlo Ghirardi Domenico J.W. Giulini Gregg Jaeger Claus Kiefer Nicolaas P. Landsman Christian Maes Hermann Nicolai Vesselin Petkov Alwyn van der Merwe Rainer Verch R.F. Werner Christian Wuthrich More information about this series at http://www.springer.com/series/6001 Xavier Calmet Editor Quantum Aspects of Black Holes 123 Editor Xavier Calmet Department of Physics and Astronomy University of Sussex Brighton UK ISBN 978-3-319-10851-3 ISBN 978-3-319-10852-0 (eBook) DOI 10.1007/978-3-319-10852-0 Library of Congress Control Number: 2014951685 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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 The decision to write this book arose in discussions among members of the Working Group 1 (WG1) of the European Cooperation in Science and Technology (COST) action MP0905 “Black Holes in a Violent Universe,” which started in 2010 and ended in May 2014. The four years of the action have been absolutely fantastic for the research themes represented by WG1. The discovery of the Higgs boson which completes the standard model of particle physics was crowned by the 2013 Nobel prize. This discovery has important implications for the unification of the standard model with general relativity which is important for Planck size black holes. Understanding at what energy scale these forces merge into a unified theory, will tell us what is the lightest possible mass for a black hole. In other words, the Large Hadron Collider (LHC) at CERN data allows us to set bounds on the Planck scale. We now know that the Planck scale is above 5 TeV. Thus, Planckian black holes are heavier than 5 TeV. The fact that no dark matter has been discovered at the LHC in the form of a new particle strengthens the assumption that primordial black holes could play that role. The data from the Planck satellite reinforce the need for inflation. Planckian black holes can make an important contribution at the earliest moment of our universe, namely during inflation if the scale at which inflation took place is close enough to the Planck scale. There have been several interesting proposals relating the Higgs boson of the standard model of particle physics with inflation. Indeed, the LHC data imply that the Higgs boson could be the inflation if the Higgs boson is non-minimally coupled to space-time curvature. In relation to the black hole information paradox, there has been much excite- ment about firewalls or what happens when an observer falls through the horizon of a black hole. However, firewalls rely on a theorem by Banks, Susskind and Peskin [Nucl. Phys. B244 (1984) 125] for which there are known counter examples as shown in 1995 by Wald and Unruh [Phys. Rev. D52 (1995) 2176–2182]. It will be interesting to see how the situation evolves in the next few years. v vi Preface These then are the reasons for writing this book, which reflects on the progress made in recent years in a field which is still developing rapidly. As well as some of the members of our working group, several other international experts have kindly agreed to contribute to the book. The result is a collection of 10 chapters dealing with different aspects of quantum effects in black holes. By quantum effects we mean both quantum mechanical effects such as Hawking radiation and quantum gravitational effects such as Planck size quantum black hole. Chapter 1 is meant to provide a broad introduction to the field of quantum effects in black holes before focusing on Planckian quantum black holes. Chapter 2 covers the thermodynamics of black holes while Chap. 3 deals with the famous information paradox. Chapter 4 discusses another type of object, so-called monsters, which have more entropy than black holes of equal mass. Primordial black holes are discussed in Chaps. 5 and 6 reviews self-gravitating Bose-Einstein condensates which open up the exciting possibility that black holes are Bose-Einstein condensates. The formation of black holes in supersymmetric theories is investigated in Chap. 7. Chapter 8 covers Hawking radiation in higher dimensional black holes. Chapter 9 presents the latest bounds on the mass of small black holes which could have been produced at the LHC. Last but not least, Chap. 10 covers non-minimal length effects in black holes. All chapters have been through a strict reviewing process. This book would not have been possible without the COST action MP0905. In particular we would like to thank Silke Britzen, the chair of our action, the members of the core group (Antxon Alberdi, Andreas Eckart, Robert Ferdman, Karl-Heinz Mack, Iossif Papadakis, Eduardo Ros, Anthony Rushton, Merja Tornikoski and Ulrike Wyputta in addition to myself) and all the members of this action for fascinating meetings and conferences. We are very grateful to Dr. Angela Lahee, our contact at Springer, for her constant support during the completion of this book. Brighton, August 2014 Xavier Calmet Contents 1 Fundamental Physics with Black Holes .................... 1 Xavier Calmet 1.1 Introduction . 1 1.2 Quantum Black Holes . 4 1.3 Low Scale Quantum Gravity and Black Holes at Colliders . 5 1.4 An Effective Theory for Quantum Gravity. 11 1.5 Quantum Black Holes in Loops . 13 1.6 Quantum Black Holes and the Unification of General Relativity and Quantum Mechanics. 16 1.7 Quantum Black Holes, Causality and Locality . 20 1.8 Conclusions . 23 References. 24 2 Black Holes and Thermodynamics: The First Half Century ..... 27 Daniel Grumiller, Robert McNees and Jakob Salzer 2.1 Introduction and Prehistory . 27 2.2 1963–1973 . 29 2.3 1973–1983 . 33 2.4 1983–1993 . 39 2.5 1993–2003 . 45 2.6 2003–2013 . 50 2.7 Conclusions and Future. 56 References. 57 3 The Firewall Phenomenon.............................. 71 R.B. Mann 3.1 Introduction . 71 3.2 Black Holes. 72 3.2.1 Gravitational Collapse . 75 3.2.2 Anti de Sitter Black Holes. 77 3.3 Black Hole Thermodynamics . 78 vii viii Contents 3.4 Black Hole Radiation . 80 3.4.1 Quantum Field Theory in Curved Spacetime . 80 3.4.2 Pair Creation . 83 3.5 The Information Paradox . 88 3.5.1 Implications of the Information Paradox . 94 3.5.2 Complementarity . 95 3.6 Firewalls . 98 3.6.1 The Firewall Argument . 98 3.6.2 Responses to the Firewall Argument . 100 3.7 Summary. 107 References. 108 4 Monsters, Black Holes and Entropy....................... 115 Stephen D.H. Hsu 4.1 Introduction . 115 4.2 What is Entropy? . 116 4.3 Constructing Monsters . 117 4.3.1 Monsters . 118 4.3.2 Kruskal–FRW Gluing . 120 4.4 Evolution and Singularities . 123 4.5 Quantum Foundations of Statistical Mechanics. 124 4.6 Statistical Mechanics of Gravity? . 126 4.7 Conclusions . 127 References. 128 5 Primordial Black Holes: Sirens of the Early Universe.......... 129 Anne M. Green 5.1 Introduction . 129 5.2 PBH Formation Mechanisms . 130 5.2.1 Large Density Fluctuations . 130 5.2.2 Cosmic String Loops . 132 5.2.3 Bubble Collisions . 132 5.3 PBH Abundance Constraints . 133 5.3.1 Evaporation . 133 5.3.2 Lensing. 135 5.3.3 Dynamical Effects . 136 5.3.4 Other Astrophysical Objects and Processes . 137 5.4 Constraints on the Primordial Power Spectrum and Inflation . 138 5.4.1 Translating Limits on the PBH Abundance into Constraints on the Primordial Power Spectrum. 139 5.4.2 Constraints on Inflation Models . 141 5.5 PBHs as Dark Matter . 142 5.6 Summary. 143 References. 144 Contents ix 6 Self-gravitating Bose-Einstein Condensates.................. 151 Pierre-Henri Chavanis 6.1 Introduction . 152 6.2 Self-gravitating Bose-Einstein Condensates . 155 6.2.1 The Gross-Pitaevskii-Poisson System .
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