Black Holes, Gravitational Radiation and the Universe Fundamental Theories of Physics

An International Book Series on The Fundamental Theories ofPhysics: Their Clarification, Development and Application

Editor: ALWYN VAN DER MERWE, University ofDenver, U.S.A.

Editoral Advisory Board: LAWRENCE P. HORWITZ, Tel-Aviv University, Israel BRIAN D. JOSEPHSON, University of Cambridge, U.K. CLIVE KILMISTER, University ofLondon, U.K. PEKKA J. LAHTI, University ofTurku, Finland GUNTER LUDWIG, Philipps-Universitiit, Marburg, Germany NATHAN ROSEN, Israel Institute ofTechnology, Israel ASHER PERES, Israel Institute of Technology, Israel EDUARD PRUGOVECKI, University of Toronto, Canada MENDEL SACHS, State University ofNew York at Buffalo, U.S.A. ABDUS SALAM, International Centre for Theoretical Physics, Trieste, Italy HANS-JURGEN TREDER, Zentralinstitutfor Astrophysik der Akademie der Wissenschaftel Germany

Volume 100 Black Holes, Gravitational Radiation and the Universe

Essays in Honor of c. V. Vishveshwara

edited by

Bala R. Iyer Raman Research Institute. Bangalore.lndia and Biplab Bhawal TAMA Project. National Astronomical Observatory. Osawa. Mitaka. Tokyo. Japan

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-90-481-5121-9 ISBN 978-94-017-0934-7 (eBook) DOI 10.1007/978-94-017-0934-7

Printed on acid-free paper

All Rights Reserved © 1999 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1999 Softcover reprint of the hardcover 1st edition 1999 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, induding photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner TABLE OF CONTENTS

Preface IX

1. The Black Hole Equilibrium Problem 1 B. Carter

2. Stability of Black Holes 17 Bernard F. Whiting

3. Separability of Wave Equations 33 E. G. Kalnins, W. Miller Jr. and G. C. Williams

4. Energy-Conservation Laws for Perturbed Stars and Black Holes 53 V. Ferrari

5. Gravitational Collapse and Cosmic Censorship 69 Robert M. Wald

6. Disturbing the Black Hole 87 Jacob D. Bekenstein

7. Notes on Black Hole Fluctuations and Back-reaction 103 B.L. Hu, Alpan Raval and Sukanya Sinha

8. Black Holes in Higher Curvature Gravity 121 R.C. Myers

9. Micro-Structure of Black Holes and String Theory 137 Spenta Wadia

10. Quantum Geometry and Black Holes 149 Abhay Ashtekar and Kirill Krasnov

11. Black Holes, Global Monopole Charge and Quasi-local Energy 171 N aresh Dadhich VI

12. Kinematical Consequences of Inertial Forces in General Relativity 189 A.R. Prasanna and Sai Iyer

13. Gyroscopic Precession and Inertial forces in General Relativity 207 Rajesh Nayak

14. Analysis of the Equilibrium of a Charged Test Particle in the Kerr-Newman Black Hole 219 J.M. Aguirregabiria, A. Chamorro and J. Suinaga

15. Neutron Stars and Relativistic Gravity 235 M. Vivekanand

16. Accretion Disks around Black Holes 249 Paul J. Wiita

17. Astrophysical Evidence for Black Hole Event Horizons 265 K. Menou, E. Quataert and R. Narayan

18. Black Holes in Active Galactic Nuclei 289 Ajit K. Kembhavi

19. Energetic Photon Spectra as Probes of the Process of Particle Acceleration in Accretion Flows around Black Holes 309 R. Cowsik

20. Black Hole Perturbation Approach to Gravitational Radiation: Post-Newtonian Expansion for Inspiralling Binaries 319 Misao Sasaki

21. More Quasi than Normal! 335 Nils Andersson

22. The Two Black Hole Problem: Beyond Linear Perturbations 351 R.H. Price

23. The Synergy between Numerical and Perturbative Approaches to Black Holes 367 Edward Seidel TABLE OF CONTENTS vii

24. Cauchy-Characteristic Matching 383 Nigel T.Bishop, Roberto Gomez, Luis Lehner, Bela Szilagyi, Jeffrey Winicour and Richard A. Isaacson

25. Astrophysical Sources of Gravitational Waves 409 B.S. Sathyaprakash

26. Gravitational Radiation from Inspiraling Compact Binaries: Motion, Generation and Radiation Reaction 437 Bala R.Iyer

27. Ground-based Interferometric Detectors of Gravitational Waves 461 Biplab Bhawal

28. Detection of Gravitational Waves from Inspiraling Compact Binaries 481 S. V. Dhurandhar

29. Perturbations of Cosmological Backgrounds 493 Peter K.S. Dunsby and George F.R. Ellis

30. Mach's Principle in Electrodynamics and Inertia 509 J ayant V. N arlikar

31. The Early History of Quantum Gravity (1916-1940) 525 John Stachel

32. Geometry in Color Perception 535 Abhay Ashtekar, Alejandro Corichi and Monica Pierri

33. C. V. Vishveshwara - A Profile 551 N. Panchapakesan

34. Publications of C. V. Vishveshwara 559

PREFACE

Our esteemed colleague C. V. Vishveshwara, popularly known as Vishu, turned sixty on 6th March 1998. His colleagues and well wishers felt that it would be appropriate to celebrate the occasion by bringing out a volume in his honour. Those of us who have had the good fortune to know Vishu, know that he is unique, in a class by himself. Having been given the privilege to be the volume's editors, we felt that we should attempt something different in this endeavour. Vishu is one of the well known relativists from India whose pioneer• ing contributions to the studies of black holes is universally recognised. He was a student of Charles Misner. His Ph. D. thesis on the stability of the Schwarzschild black hole, coordinate invariant characterisation of the sta• tionary limit and event horizon for Kerr black holes and subsequent seminal work on quasi-normal modes of black holes have passed on to become the starting points for detailed mathematical investigations on the nature of black holes. He later worked on other aspects related to black holes and compact objects. Many of these topics have matured over the last thirty years. New facets have also developed and become current areas of vigorous research interest. No longer are black holes, ultracompact objects or event horizons mere idealisations of mathematical physicists but concrete entities that astrophysicists detect, measure and look for. Astrophysical evidence is mounting up steadily for black holes. The laser interferometric gravita• tional wave experiments, LIGO and VIRGO, under way in the USA and Europe respectively, should be completed by 2001 and could provide our first direct detection of gravitational waves from binary black hole systems. There are new concrete proposals for quantum theories of gravity with deep implications for the microstructure of black holes. We felt that the time was just right to assess the progress made in these various topics of black hole research via short reviews by respective experts. Thus instead of being a collection of many different topics the volume would weave separate threads into the majestic black hole tapestry. We have attempted to carefully plan the volume with a view of making it uniform and useful. This we felt would give Vishu great pleasure since it could have a longer term pedagogic value and prove to be useful to the relativity community in general, especially fresh graduate students, fresh post docs and other research scientists. This attempt is our personal tribute to Vishu on behalf of all those numerous colleagues, students and x lay persons who have been touched by the magic realism of his popular talks, humour and deep erudition .. We hope the volume leads the reader along a seemingly lazy innocuous trail that began in the sixties, through today, to the future. It is an attempt to offer a grand panoramic view of black hole physics before the new millennium. We were gratified with the warm response we received from all the contributors to our request to write for the volume. Some of them have known Vishu personally for a long time, others just via his papers. It was gratifying to find the international relativity community as a whole, still like one huge extended family bound by wonderful emotions and a sense of common endeavour, regardless of age or any other divisive factors. We thank our contributing colleagues for their critical and thorough assessments of the areas of their speciality and their participation in The Fest at the GR15 at lUCCA, Pune, in December 1997. A word of explanation is in order in regard to two articles by Abhay Ashtekar in the book. While the book was in its final stages the exciting work on implications of nonperturbative quantum gravity for black hole entropy appeared and we felt that this must be reviewed in the volume. Though Abhay had already sent us his contribution to the Fest earlier, we are happy that Abhay and Krasnov graciously agreed to our suggestion to write the review at very short notice. It is a pleasure to thank G. Manjunatha for his meticulous, enthusiastic and uncomplaining assistence over the last few months, in preparing this volume for publication. We thank B. S. Gujjarappa for the caricature of Vishu that appears in these proceedings and Raju Verghese for producing the photographic prints in the volume. We thank A. Ratnakar for his assis• tence in checking the publication list of C. V. Vishveshwara, and Sai lyer and A. Gopakumar for help with preparing some articles for production. We acknowledge the cooperation of our publishers Kluwer Academic Pub• lishers, The Netherlands and in particular Dr. David Lamer and Margaret Deignan in bringing out this volume. We would like to express our appre• ciation of Kluwer's attempts to publish highly specialised books and serve this relatively small academic community.

Bala lyer Biplab Bhawal BIBLIOGRAPHICAL NOTES

The quotations in the book are from the following sources:

1. C. Behr, E. L. Schucking, C. V. Vishveshwara and W. Wallace, Kinematics of Relativistic Ejection, Astronom. Journ., 81, 147 (1976). 2. Thibault Damour, The problem of motion in Newtonian and Einsteinian grav• ity, in '300 years of Gravitation', eds. S. W. Hawking and W. Israel ( CUP, Cambridge, 1987). 3. Robert H. Dicke in The Theoretical Significance of Experimental Relativity (1964). 4. F. A. E. Pirani, Gravitational radiation, in 'Gravitation: An introduction to current research', ed. L. Witten, (Wiley, 1962). 5. B. Rossi, Preface to X-ray Astronomy, ed. R. Giaconni and H. Gursky, Dor• drecht, Reidel (1974). 6. Kip Thorne, Black holes and time warps, W. W. Norton and Co. (1994). 7. C. V. Vishveshwara, Black Holes for Bedtime, in 'Gravitation, Quanta and the Universe', eds. A. R. Prasanna, J. V. Narlikar and C. V. Vishveshwara (Wiley Eastern, 1980), 8. C. V. Vishveshwara, The Engelbert Experience: Pathways from the past, in 'On Einstein's Path: Essays in Honor of Engelbert Schucking', eds. Alex Har• vey (Springer-Verlag, 1998). 9. C. V. Vishveshwara, After the Fall: From Adam and Eve to Apples and Ele• vators, in 'Gravitational and Cosmology: At the Turn of the Millenium', eds. N. K. Dadhich and J. V. Narlikar (IUCAA, Pune, 1998). 10. John Wheeler, in Black holes and time warps, Kip Thorne, W. W. Norton and Co. (1994). 11. Clifford M. Will in Was Einstein right? (Oxford, 1986)