DOCSLIB.ORG

Holography for Black Holes in General Relativity and Beyond

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Holography for Black Holes in General Relativity and Beyond Holography for Black Holes in General Relativity and Beyond A Thesis Submitted to the College of Graduate and Postdoctoral Studies in Partial Fulfillment of the Requirements for the degree of Master of Science in the Department of Physics & Engineering Physics University of Saskatchewan Saskatoon By Canisius Bernard c Canisius Bernard, August 2020. All rights reserved. Permission to Use In presenting this thesis in partial fulfilment of the requirements for a Postgraduate degree from the University of Saskatchewan, I agree that the Libraries of this University may make it freely available for inspection. I further agree that permission for copying of this thesis in any manner, in whole or in part, for scholarly purposes may be granted by the professor or professors who supervised my thesis work or, in their absence, by the Head of the Department or the Dean of the College in which my thesis work was done. It is understood that any copying or publication or use of this thesis or parts thereof for financial gain shall not be allowed without my written permission. It is also understood that due recognition shall be given to me and to the University of Saskatchewan in any scholarly use which may be made of any material in my thesis. Requests for permission to copy or to make other use of material in this thesis in whole or part should be addressed to: Head of the Department Department of Physics and Engineering Physics University of Saskatchewan 163 Physics Building, 116 Science Place Saskatoon, Saskatchewan S7N 5E2 Canada or Dean College of Graduate and Postdoctoral Studies University of Saskatchewan 116 Thorvaldson Building, 110 Science Place Saskatoon, Saskatchewan S7N 5C9 Canada i Abstract Both extremal and non-extremal Kerr black holes have been considered to be holographically dual to two-dimensional (2D) conformal field theories (CFTs). In this thesis, we study the holography to the case of a rotating Janis-Newman-Winicour (JNW) black holes, a rotating Brans-Dicke-Kerr (BDK) black hole, and an asymptotically anti-de Sitter (AdS) rotating charged black holes in f(T ) gravity, where f(T ) = T + αT 2, where α is a constant. Firstly, we find that the rotating JNW solution does not satisfy the Einstein field equation. Thus, we could not establish a well-defined Kerr/CFT correspondence in this theory. Secondly, we find that the scalar wave equation in the background of BDK black hole is not separable. The existence of the SL(2;R)L × SL(2;R)R symmetry can be found in the radial equation of the scalar probe around the non-extremal black hole. Therefore, the inseparability of the scalar wave equation eliminates the possibility of any holography aspect for BDK black hole. Thirdly, we find that the scalar wave radial equation at the near-horizon region implies the existence of the 2D conformal symmetries. We note that the 2π identification of the azimuthal angle φ in the black hole line element, corresponds to a spontaneous breaking of the conformal symmetry by left and right temperatures TL and TR, respectively. We show that choosing proper central charges for the dual CFT, we produce exactly the macroscopic Bekenstein-Hawking entropy from the microscopic Cardy entropy for the dual CFT. These observations suggest that the rotating charged AdS black hole in f(T ) gravity is dual to a 2D CFT at finite temperatures TL and TR for a specific value of mass M, rotational, charge, and f(T ) parameters, Ω, Q, and jαj, respectively. ii Acknowledgements I am deeply grateful to my academic supervisor, Prof. Masoud Ghezelbash, for his invaluable help, mo- tivation, enthusiasm, patience, and immense knowledge he has provided throughout my time as his student. I would like to thank my advisory committee members, Prof. Rainer Dick, Prof. Rob Pywell, and Prof. Robert Green for their guidance and insightful comments. I would like to thank Prof. Steven Rayan, who acted as the external examiner in my defence. I also thank the Department of Physics and Engineering Physics secretaries, Deborah Gjertsen and Marjorie Granrude, for their administrative supports and con- stant attention. I am indebted to my mentor, Dr. Haryanto Siahaan, for his tremendous help, advice, and continuing encouragement. My journey to Canada would not have been possible without the support of my parents, Margaretha C. Sugiharti and Suryamin Maryadi, my aunts Maria E. M. Hegarwati and Miranda Maryadi, my uncles Anto- nius Yuliono and Erwin Budiman, my grandparents Paulus Kutomiharso and Veronica Kang, Andi Maryadi and Sisiliawati. No thanks can be adequate for the decades of their loving support and understanding. My special thank goes to numerous friends in the Department of Physics and Engineering Physics, among them Jeffery Zielinski, William Elcock, Patrick Braun, Alex Chang, Bardia Fahim, Niyusha Hoseiny, Ayub Khodaee, Marilyn Jimenez, Oleksandr Chapurin, Barbara Cid Mora, and Siyuan Li. I would like to thank Jeffery Zielinski for his constructive criticism of the thesis, help, advice, and useful discussion. Some special words of gratitude also go to my friends Saga Bergqvist, Len Song, and Mengying Liu. They have contributed in many different ways during the writing up of this thesis. Last but not least, I would like to thank the Indonesian community in Saskatoon for their warm welcome, hospitality, constant support, and attention. During the course of this work, I was supported by the Natural Sciences and Engineering Research Council of Canada, University of Saskatchewan Graduate Teaching Fellowships, and William Rowles Fellowship in Physics and Engineering Physics. I am very grateful to all these organizations. Canisius Bernard Saskatoon, Canada iii To my parents \Ipsa scientia potestas est." | Sir Francis Bacon, Meditationes sacrae iv Contents Permission to Use i Abstract ii Acknowledgements iii Dedication iv Contents v List of Figures vii List of Abbreviations viii 1 Introduction 1 2 Black Holes in Einstein Gravity and Beyond 5 2.1 Einstein gravity . 5 2.1.1 A variational approach to general relativity . 6 2.1.2 Kerr black holes . 10 2.1.3 The law of thermodynamics and black holes mechanics . 16 2.2 Gravity with torsion . 18 2.2.1 Torsion tensor . 19 2.2.2 Teleparallel equivalent of general relativity and the f(T ) extension . 20 2.2.3 Black holes in quadratic f(T ) gravity . 25 3 Introducing Conformal Field Theory 28 3.1 Conformal group in N > 2 dimensions . 28 3.2 Conformal group in N = 2 dimensions . 30 3.2.1 The central charge and the Virasoro algebra . 33 3.2.2 Energy-momentum tensor and Noether currents . 35 3.2.3 Primary fields . 38 3.2.4 Conformal field theory properties on an infinite cylinder . 39 3.2.5 Conformal field theory on the torus . 40 3.2.6 Cardy entropy . 42 4 Holographic Aspects of Kerr Black Holes 45 4.1 Extremal Kerr black hole and holography . 45 4.1.1 AdS3 and SL(2;R)L × SL(2;R)R .............................. 45 4.1.2 SL(2;R) Lie algebra . 46 4.1.3 AdS3/CFT2 correspondence . 47 4.1.4 Kerr/CFT correspondence . 47 4.2 Non-extremal Kerr black hole and holography . 49 4.2.1 Scalar scattering off a Kerr black hole . 49 4.2.2 Hidden conformal symmetry . 50 4.2.3 Temperature and entropy in conformal field theory . 52 5 Holographic Aspects of Black Holes in Modified Gravity 54 5.1 Is there a hidden conformal symmetry for black holes in scalar-tensor gravity? . 54 5.1.1 Scalar scattering off a Janis-Newman-Winicour black hole . 54 v 5.1.2 Validity of rotating Janis-Newman-Winicour spacetime . 57 5.1.3 Scalar scattering off a Brans-Dicke-Kerr black hole . 58 5.2 Hidden conformal symmetry of black holes in f(T ) gravity . 60 5.2.1 Rotating charged AdS black holes . 60 5.2.2 The first law of black hole thermodynamics . 61 5.2.3 Scalar scattering off a rotating charged AdS black hole . 65 5.2.4 Hidden conformal symmetry . 67 5.2.5 Cardy entropy . 72 6 Conclusion 75 References 78 vi List of Figures 1.1 Event Horizon Telescope image of the Messier 87 black hole shadow. This figure is taken from Ref. [1]. 1 1.2 Extremal Kerr black hole illustration. 3 2.1 Illustration of a Kerr black hole. 15 µ 2.2 Four-dimensional spacetime manifold M with a metric gµν where tetrad fields eA = eA@µ are defined at point p on the tangent space TP ............................. 19 3.1 Projecting S2 to C2 illustration. 32 3.2 Cylinder to complex plane mapping illustration. 39 3.3 Lattice of a torus. 40 3.4 Modular S-transformation on lattice of a torus. 42 5.1 φ~ as a function of (a) r with θ = π, (b) θ with r = 1, both with a = 1, M = 0:1, and several numerical values of γ. ........................................ 56 5.2 A(r) as a function of r with M = 5;Q = 0:1; and several numerical values of jαj. 61 5.3 S as a function of M and Q. In these plots, we set Ω = 1; l = 1; jαj = 0:05;L = 1; and r+ = 1. 64 5.4 S as a function of (a) Ω with l = 1, α = 0:05, and several numerical values of M. (b) jαj with M = 3:5, Ω = 1, and several numerical values of l, both with Q = 1, L = 1, and r+ = 1. 65 5.5 Equations (5.80) and (5.81), respectively, as a function of Q. In this plot, we set, M = 5; Ω = 1; l = 1; jαj = 0:05; and r+ = 2:08.
Load more

Recommended publications
  • Selected Papers on Teleparallelism Ii
    SELECTED PAPERS ON TELEPARALLELISM Edited and translated by D. H. Delphenich Table of contents Page Introduction ……………………………………………………………………… 1 1. The unification of gravitation and electromagnetism 1 2. The geometry of parallelizable manifold 7 3. The field equations 20 4. The topology of parallelizability 24 5. Teleparallelism and the Dirac equation 28 6. Singular teleparallelism 29 References ……………………………………………………………………….. 33 Translations and time line 1928: A. Einstein, “Riemannian geometry, while maintaining the notion of teleparallelism ,” Sitzber. Preuss. Akad. Wiss. 17 (1928), 217- 221………………………………………………………………………………. 35 (Received on June 7) A. Einstein, “A new possibility for a unified field theory of gravitation and electromagnetism” Sitzber. Preuss. Akad. Wiss. 17 (1928), 224-227………… 42 (Received on June 14) R. Weitzenböck, “Differential invariants in EINSTEIN’s theory of teleparallelism,” Sitzber. Preuss. Akad. Wiss. 17 (1928), 466-474……………… 46 (Received on Oct 18) 1929: E. Bortolotti , “ Stars of congruences and absolute parallelism: Geometric basis for a recent theory of Einstein ,” Rend. Reale Acc. dei Lincei 9 (1929), 530- 538...…………………………………………………………………………….. 56 R. Zaycoff, “On the foundations of a new field theory of A. Einstein,” Zeit. Phys. 53 (1929), 719-728…………………………………………………............ 64 (Received on January 13) Hans Reichenbach, “On the classification of the new Einstein Ansatz on gravitation and electricity,” Zeit. Phys. 53 (1929), 683-689…………………….. 76 (Received on January 22) Selected papers on teleparallelism ii A. Einstein, “On unified field theory,” Sitzber. Preuss. Akad. Wiss. 18 (1929), 2-7……………………………………………………………………………….. 82 (Received on Jan 30) R. Zaycoff, “On the foundations of a new field theory of A. Einstein; (Second part),” Zeit. Phys. 54 (1929), 590-593…………………………………………… 89 (Received on March 4) R.
    [Show full text]
  • Book of Abstracts Ii Contents
    Spring workshop on gravity and cosmology Monday, 25 May 2020 - Friday, 29 May 2020 Jagiellonian University Book of Abstracts ii Contents Stochastic gravitational waves from inflaton decays ..................... 1 Approximate Killing symmetries in non-perturbative quantum gravity .......... 1 Disformal transformations in modified teleparallelism .................... 1 Quantum fate of the BKL scenario ............................... 2 Ongoing Efforts to Constrain Lorentz Symmetry Violation in Gravity ........... 2 Proof of the quantum null energy condition for free fermionic field theories . 2 Cosmic Fibers and the parametrization of time in CDT quantum gravity . 3 Stable Cosmology in Generalised Massive Gravity ...................... 3 Constraining the inflationary field content .......................... 3 The (glorious) past, (exciting) present and (foreseeable) future of gravitational wave detec- tors. ............................................. 4 reception ............................................. 4 Testing Inflation with Primordial Messengers ........................ 4 Gravitational waves from inflation ............................... 4 CDT, a theory of quantum geometry. ............................. 4 Cosmic Fibers and the parametrization of time in CDT quantum gravity . 5 Loop-based observables in 4D CDT .............................. 5 Spectral Analysis of Causal Dynamical Triangulations via Finite Element Methods . 5 A consistent theory of D -> 4 Einstein-Gauss-Bonnet gravity ................ 5 Quantum Ostrogradsky theorem
    [Show full text]
  • Cracking the Einstein Code: Relativity and the Birth of Black Hole Physics, with an Afterword by Roy Kerr / Fulvio Melia
    CRA C K I N G T H E E INSTEIN CODE @SZObWdWbgO\RbVS0W`bV]T0ZOQY6]ZS>VgaWQa eWbVO\/TbS`e]`RPg@]gS`` fulvio melia The University of Chicago Press chicago and london fulvio melia is a professor in the departments of physics and astronomy at the University of Arizona. He is the author of The Galactic Supermassive Black Hole; The Black Hole at the Center of Our Galaxy; The Edge of Infinity; and Electrodynamics, and he is series editor of the book series Theoretical Astrophysics published by the University of Chicago Press. The University of Chicago Press, Chicago 60637 The University of Chicago Press, Ltd., London © 2009 by The University of Chicago All rights reserved. Published 2009 Printed in the United States of America 18 17 16 15 14 13 12 11 10 09 1 2 3 4 5 isbn-13: 978-0-226-51951-7 (cloth) isbn-10: 0-226-51951-1 (cloth) Library of Congress Cataloging-in-Publication Data Melia, Fulvio. Cracking the Einstein code: relativity and the birth of black hole physics, with an afterword by Roy Kerr / Fulvio Melia. p. cm. Includes bibliographical references and index. isbn-13: 978-0-226-51951-7 (cloth: alk. paper) isbn-10: 0-226-51951-1 (cloth: alk. paper) 1. Einstein field equations. 2. Kerr, R. P. (Roy P.). 3. Kerr black holes—Mathematical models. 4. Black holes (Astronomy)—Mathematical models. I. Title. qc173.6.m434 2009 530.11—dc22 2008044006 To natalina panaia and cesare melia, in loving memory CONTENTS preface ix 1 Einstein’s Code 1 2 Space and Time 5 3 Gravity 15 4 Four Pillars and a Prayer 24 5 An Unbreakable Code 39 6 Roy Kerr 54 7 The Kerr Solution 69 8 Black Hole 82 9 The Tower 100 10 New Zealand 105 11 Kerr in the Cosmos 111 12 Future Breakthrough 121 afterword 125 references 129 index 133 PREFACE Something quite remarkable arrived in my mail during the summer of 2004.
    [Show full text]
  • The Emergence of Gravitational Wave Science: 100 Years of Development of Mathematical Theory, Detectors, Numerical Algorithms, and Data Analysis Tools
    BULLETIN (New Series) OF THE AMERICAN MATHEMATICAL SOCIETY Volume 53, Number 4, October 2016, Pages 513–554 http://dx.doi.org/10.1090/bull/1544 Article electronically published on August 2, 2016 THE EMERGENCE OF GRAVITATIONAL WAVE SCIENCE: 100 YEARS OF DEVELOPMENT OF MATHEMATICAL THEORY, DETECTORS, NUMERICAL ALGORITHMS, AND DATA ANALYSIS TOOLS MICHAEL HOLST, OLIVIER SARBACH, MANUEL TIGLIO, AND MICHELE VALLISNERI In memory of Sergio Dain Abstract. On September 14, 2015, the newly upgraded Laser Interferometer Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW) signal, emitted a billion light-years away by a coalescing binary of two stellar-mass black holes. The detection was announced in February 2016, in time for the hundredth anniversary of Einstein’s prediction of GWs within the theory of general relativity (GR). The signal represents the first direct detec- tion of GWs, the first observation of a black-hole binary, and the first test of GR in its strong-field, high-velocity, nonlinear regime. In the remainder of its first observing run, LIGO observed two more signals from black-hole bina- ries, one moderately loud, another at the boundary of statistical significance. The detections mark the end of a decades-long quest and the beginning of GW astronomy: finally, we are able to probe the unseen, electromagnetically dark Universe by listening to it. In this article, we present a short historical overview of GW science: this young discipline combines GR, arguably the crowning achievement of classical physics, with record-setting, ultra-low-noise laser interferometry, and with some of the most powerful developments in the theory of differential geometry, partial differential equations, high-performance computation, numerical analysis, signal processing, statistical inference, and data science.
    [Show full text]
  • Modified Theories of Relativistic Gravity
    Modified Theories of Relativistic Gravity: Theoretical Foundations, Phenomenology, and Applications in Physical Cosmology by c David Wenjie Tian A thesis submitted to the School of Graduate Studies in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Theoretical Physics (Interdisciplinary Program) Faculty of Science Date of graduation: October 2016 Memorial University of Newfoundland March 2016 St. John’s Newfoundland and Labrador Abstract This thesis studies the theories and phenomenology of modified gravity, along with their applications in cosmology, astrophysics, and effective dark energy. This thesis is organized as follows. Chapter 1 reviews the fundamentals of relativistic gravity and cosmology, and Chapter 2 provides the required Co-authorship 2 2 Statement for Chapters 3 ∼ 6. Chapter 3 develops the L = f (R; Rc; Rm; Lm) class of modified gravity 2 µν 2 µανβ that allows for nonminimal matter-curvature couplings (Rc B RµνR , Rm B RµανβR ), derives the “co- herence condition” f 2 = f 2 = − f 2 =4 for the smooth limit to f (R; G; ) generalized Gauss-Bonnet R Rm Rc Lm gravity, and examines stress-energy-momentum conservation in more generic f (R; R1;:::; Rn; Lm) grav- ity. Chapter 4 proposes a unified formulation to derive the Friedmann equations from (non)equilibrium (eff) thermodynamics for modified gravities Rµν − Rgµν=2 = 8πGeffTµν , and applies this formulation to the Friedman-Robertson-Walker Universe governed by f (R), generalized Brans-Dicke, scalar-tensor-chameleon, quadratic, f (R; G) generalized Gauss-Bonnet and dynamical Chern-Simons gravities. Chapter 5 systemati- cally restudies the thermodynamics of the Universe in ΛCDM and modified gravities by requiring its com- patibility with the holographic-style gravitational equations, where possible solutions to the long-standing confusions regarding the temperature of the cosmological apparent horizon and the failure of the second law of thermodynamics are proposed.
    [Show full text]
  • Alternative Gravitational Theories in Four Dimensions
    Alternative Gravitational Theories in Four Dimensionsa Friedrich W. Hehl Institute for Theoretical Physics, University of Cologne, D-50923 K¨oln, Germany email: [email protected] We argue that from the point of view of gauge theory and of an appropriate interpretation of the interferometer experiments with matter waves in a gravitational field, the Einstein- Cartan theory is the best theory of gravity available. Alternative viable theories are general relativity and a certain teleparallelism model. Objections of Ohanian & Ruffini against the Einstein-Cartan theory are discussed. Subsequently we list the papers which were read at the ‘Alternative 4D Session’ and try to order them, at least partially, in the light of the structures discussed. 1 The best alternative theory? I would call general relativity theory8 GR the best available alternative gravitational 21,14 theory and the next best one its teleparallel equivalent GR||. Because of these two theories, at least, it is good to have this alternative session during the Marcel Grossmann Meeting. Let me try to explain why I grant to GR the distinction of being the best alternative theory. After finally having set up special relativity theory in 1905, Einstein subse- quently addressed the question of how to generalize Newton’s gravitational theory as to make it consistent with special relativity, that is, how to reformulate it in a Poincar´ecovariant way. Newton’s theory was a battle tested theory in the realm of our planetary system and under normal laboratory conditions. It has predictive power as it had been shown by the prediction of the existence of the planet Neptune in the last century.
    [Show full text]
  • Teleparallelism Arxiv:1506.03654V1 [Physics.Pop-Ph] 11 Jun 2015
    Teleparallelism A New Way to Think the Gravitational Interactiony At the time it celebrates one century of existence, general relativity | Einstein's theory for gravitation | is given a companion theory: the so-called teleparallel gravity, or teleparallelism for short. This new theory is fully equivalent to general relativity in what concerns physical results, but is deeply different from the con- ceptual point of view. Its characteristics make of teleparallel gravity an appealing theory, which provides an entirely new way to think the gravitational interaction. R. Aldrovandi and J. G. Pereira Instituto de F´ısica Te´orica Universidade Estadual Paulista S~aoPaulo, Brazil arXiv:1506.03654v1 [physics.pop-ph] 11 Jun 2015 y English translation of the Portuguese version published in Ci^enciaHoje 55 (326), 32 (2015). 1 Gravitation is universal One of the most intriguing properties of the gravitational interaction is its universality. This hallmark states that all particles of nature feel gravity the same, independently of their masses and of the matter they are constituted. If the initial conditions of a motion are the same, all particles will follow the same trajectory when submitted to a gravitational field. The origin of universality is related to the concept of mass. In principle, there should exist two different kinds of mass: the inertial mass mi and the gravitational mass mg. The inertial mass would describe the resistance a particle shows whenever one attempts to change its state of motion, whereas the gravitational mass would describe how a particle reacts to the presence of a gravitational field. Particles with different relations mg=mi, therefore, should feel gravity differently when submitted to a given gravitational field.
    [Show full text]
  • Spacetime Warps and the Quantum World: Speculations About the Future∗
    Spacetime Warps and the Quantum World: Speculations about the Future∗ Kip S. Thorne I’ve just been through an overwhelming birthday celebration. There are two dangers in such celebrations, my friend Jim Hartle tells me. The first is that your friends will embarrass you by exaggerating your achieve- ments. The second is that they won’t exaggerate. Fortunately, my friends exaggerated. To the extent that there are kernels of truth in their exaggerations, many of those kernels were planted by John Wheeler. John was my mentor in writing, mentoring, and research. He began as my Ph.D. thesis advisor at Princeton University nearly forty years ago and then became a close friend, a collaborator in writing two books, and a lifelong inspiration. My sixtieth birthday celebration reminds me so much of our celebration of Johnnie’s sixtieth, thirty years ago. As I look back on my four decades of life in physics, I’m struck by the enormous changes in our under- standing of the Universe. What further discoveries will the next four decades bring? Today I will speculate on some of the big discoveries in those fields of physics in which I’ve been working. My predictions may look silly in hindsight, 40 years hence. But I’ve never minded looking silly, and predictions can stimulate research. Imagine hordes of youths setting out to prove me wrong! I’ll begin by reminding you about the foundations for the fields in which I have been working. I work, in part, on the theory of general relativity. Relativity was the first twentieth-century revolution in our understanding of the laws that govern the universe, the laws of physics.
    [Show full text]
  • Listening for Einstein's Ripples in the Fabric of the Universe
    Listening for Einstein's Ripples in the Fabric of the Universe UNCW College Day, 2016 Dr. R. L. Herman, UNCW Mathematics & Statistics/Physics & Physical Oceanography October 29, 2016 https://cplberry.com/2016/02/11/gw150914/ Gravitational Waves R. L. Herman Oct 29, 2016 1/34 Outline February, 11, 2016: Scientists announce first detection of gravitational waves. Einstein was right! 1 Gravitation 2 General Relativity 3 Search for Gravitational Waves 4 Detection of GWs - LIGO 5 GWs Detected! Figure: Person of the Century. Gravitational Waves R. L. Herman Oct 29, 2016 2/34 Isaac Newton (1642-1727) In 1680s Newton sought to present derivation of Kepler's planetary laws of motion. Principia 1687. Took 18 months. Laws of Motion. Law of Gravitation. Space and time absolute. Figure: The Principia. Gravitational Waves R. L. Herman Oct 29, 2016 3/34 James Clerk Maxwell (1831-1879) - EM Waves Figure: Equations of Electricity and Magnetism. Gravitational Waves R. L. Herman Oct 29, 2016 4/34 Special Relativity - 1905 ... and then came A. Einstein! Annus mirabilis papers. Special Relativity. Inspired by Maxwell's Theory. Time dilation. Length contraction. Space and Time relative - Flat spacetime. Brownian motion. Photoelectric effect. E = mc2: Figure: Einstein (1879-1955) Gravitational Waves R. L. Herman Oct 29, 2016 5/34 General Relativity - 1915 Einstein generalized special relativity for Curved Spacetime. Einstein's Equation Gravity = Geometry Gµν = 8πGTµν: Mass tells space how to bend and space tell mass how to move. Predictions. Perihelion of Mercury. Bending of Light. Time dilation. Inspired by his "happiest thought." Gravitational Waves R. L. Herman Oct 29, 2016 6/34 The Equivalence Principle Bodies freely falling in a gravitational field all accelerate at the same rate.
    [Show full text]
  • Complex Spacetimes and the Newman-Janis Trick Arxiv
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by ResearchArchive at Victoria University of Wellington Complex Spacetimes and the Newman-Janis Trick Deloshan Nawarajan VICTORIAUNIVERSITYOFWELLINGTON Te Whare Wananga¯ o te UpokooteIkaaM¯ aui¯ School of Mathematics and Statistics Te Kura Matai¯ Tatauranga arXiv:1601.03862v1 [gr-qc] 15 Jan 2016 A thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Master of Science in Mathematics. Victoria University of Wellington 2015 Abstract In this thesis, we explore the subject of complex spacetimes, in which the math- ematical theory of complex manifolds gets modified for application to General Relativity. We will also explore the mysterious Newman-Janis trick, which is an elementary and quite short method to obtain the Kerr black hole from the Schwarzschild black hole through the use of complex variables. This exposition will cover variations of the Newman-Janis trick, partial explanations, as well as original contributions. Acknowledgements I want to thank my supervisor Professor Matt Visser for many things, but three things in particular. First, I want to thank him for taking me on board as his research student and providing me with an opportunity, when it was not a trivial decision. I am forever grateful for that. I also want to thank Matt for his amazing support as a supervisor for this research project. This includes his time spent on this project, as well as teaching me on other current issues of theoretical physics and shaping my understanding of the Universe. I couldn’t have asked for a better mentor.
    [Show full text]
  • 1 the Warped Science of Interstellar Jean
    The Warped Science of Interstellar Jean-Pierre Luminet Aix-Marseille Université, CNRS, Laboratoire d'Astrophysique de Marseille (LAM) UMR 7326 Centre de Physique Théorique de Marseille (CPT) UMR 7332 and Observatoire de Paris (LUTH) UMR 8102 France E-mail: [email protected] The science fiction film, Interstellar, tells the story of a team of astronauts searching a distant galaxy for habitable planets to colonize. Interstellar’s story draws heavily from contemporary science. The film makes reference to a range of topics, from established concepts such as fast-spinning black holes, accretion disks, tidal effects, and time dilation, to far more speculative ideas such as wormholes, time travel, additional space dimensions, and the theory of everything. The aim of this article is to decipher some of the scientific notions which support the framework of the movie. INTRODUCTION The science-fiction movie Interstellar (2014) tells the adventures of a group of explorers who use a wormhole to cross intergalactic distances and find potentially habitable exoplanets to colonize. Interstellar is a fiction, obeying its own rules of artistic license : the film director Christopher Nolan and the screenwriter, his brother Jonah, did not intended to put on the screens a documentary on astrophysics – they rather wanted to produce a blockbuster, and they succeeded pretty well on this point. However, for the scientific part, they have collaborated with the physicist Kip Thorne, a world-known specialist in general relativity and black hole theory. With such an advisor, the promotion of the movie insisted a lot on the scientific realism of the story, in particular on black hole images calculated by Kip Thorne and the team of visual effects company Double Negative.
    [Show full text]
  • PHY390, the Kerr Metric and Black Holes
    PHY390, The Kerr Metric and Black Holes James Lattimer Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University April 1, 2021 Black Holes, Neutron Stars and Gravitational Radiation [email protected] James Lattimer PHY390, The Kerr Metric and Black Holes What Exactly is a Black Hole? Standard definition: A region of space from which nothing, not even light, can escape. I Where does the escape velocity equal the speed of light? r 2GMBH vesc = = c RSch This defines the Schwarzschild radius RSch to be 2GMBH M RSch = 2 ' 3 km c M I The event horizon marks the point of no return for any object. I A black hole is black because it absorbs everything incident on the event horizon and reflects nothing. I Black holes are hypothesized to form in three ways: I Gravitational collapse of a star I A high energy collision I Density fluctuations in the early universe I In general relativity, the black hole's mass is concentrated at the center in a singularity of infinite density. James Lattimer PHY390, The Kerr Metric and Black Holes John Michell and Black Holes The first reference is by the Anglican priest, John Michell (1724-1793), in a letter written to Henry Cavendish, of the Royal Society, in 1783. He reasoned, from observations of radiation pressure, that light, like mass, has inertia. If gravity affects light like its mass equivalent, light would be weakened. He argued that a Sun with 500 times its radius and the same density would be so massive that it's escape velocity would exceed light speed.
    [Show full text]