DOCSLIB.ORG

Traversable Wormholes and Regenesis

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Traversable Wormholes and Regenesis Traversable Wormholes and Regenesis The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Gao, Ping. 2019. Traversable Wormholes and Regenesis. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:42029626 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA Traversable Wormholes and Regenesis A dissertation presented by Ping Gao to The Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Physics Harvard University Cambridge, Massachusetts April 2019 c 2019 | Ping Gao All rights reserved. Dissertation Advisor: Daniel Louis Jafferis Ping Gao Traversable Wormholes and Regenesis Abstract In this dissertation we study a novel solution of traversable wormholes in the context of AdS/CFT. This type of traversable wormhole is the first such solution that has been shown to be embeddable in a UV complete theory of gravity. We discuss its property from points of view of both semiclassical gravity and general chaotic system. On gravity side, after turning on an interaction that couples the two boundaries of an eternal BTZ black hole, in chapter 2 we find a quantum matter stress tensor with negative average null energy, whose gravitational backreaction renders the Einstein-Rosen bridge traversable. Such a traversable wormhole has an interesting interpretation in the context of ER=EPR, which we suggest might be related to quantum teleportation. However, it cannot be used to violate causality. We also discuss the implications for the energy and holographic entropy in the dual CFT description. The gravity solution of this traversable wormhole indicates that in holographic systems signals generated by a source could reappear long after they have dissipated, with the need of only performing some simple operations. In chapter 3, we argue the phenomenon, to which we refer as \regenesis", is universal in general quantum chaotic many-body systems, and elucidate its underlying physics. The essential elements behind the phenomenon are: (i) scrambling which in a chaotic system makes out-of-time-ordered correlation functions (OTOCs) vanish at large times; (ii) the entanglement structure of the state of the system. The latter aspect also implies that the regenesis phenomenon requires fine tuning of the initial state. Compared to other manifestations of quantum chaos such as the initial growth of OTOCs which deals with early times, and a random matrix-type energy spectrum which reflects very large time behavior, regenesis concerns with intermediate times, of order the scrambling time of a system. We also study the phenomenon in detail in general two-dimensional conformal field theories in the large central charge limit, and highlight some interesting features including a resonant enhancement of regenesis signals near the scrambling time and their oscillations in coupling. Finally, we discuss gravity implications of the phenomenon for systems with a gravity dual, arguing that there exist regimes for which traversability of a wormhole is quantum in nature, i.e. cannot be associated with a semi-classical spacetime causal structure. iii iv Contents Abstract iii Citations to previously published work viii Acknowledgments ix Dedication xi 1 Introduction and Summary1 2 Traversable Wormholes via a Double Trace Deformation7 2.1 Introduction....................................7 2.2 Modified bulk two-point function........................ 12 2.3 1-loop stress tensor................................ 15 2.4 Holographic Energy and Entropy........................ 20 2.5 Discussion..................................... 23 R 2.A dUTUU ...................................... 29 3 Regenesis and Quantum Traversable Wormholes 33 3.1 Introduction.................................... 33 3.2 A general argument for the regenesis phenomenon............... 39 v CONTENTS 3.2.1 More on the general setup........................ 39 3.2.2 Entanglement structure......................... 40 3.2.3 Regenesis behavior for quantum chaotic systems............ 41 3.2.4 Quantum nature of the regenesis signal................. 44 3.2.5 Robustness of the regenesis phenomenon................ 46 3.2.6 A contrast study: \regenesis" in a qubit model............. 48 3.2.7 A generalization: regenesis between spatially separated points.... 51 3.3 Explicit computations in large c CFTs..................... 51 3.3.1 Some useful expressions......................... 52 3.3.2 More elaborations on W ......................... 53 3.3.3 Evaluating W : part I........................... 53 3.3.4 Evaluating W : part II.......................... 56 3.4 Analysis of the results.............................. 57 3.4.1 General remarks............................. 57 3.4.2 A scaling limit.............................. 60 3.4.3 Three regimes of GLR ........................... 61 3.4.4 Multiple channel from integration.................... 63 3.4.5 Robustness of regenesis from CFT calculations............. 65 3.5 Gravity interpretation.............................. 66 3.5.1 Explicit comparison with gravity results................ 68 3.5.2 A semi-classical regime.......................... 70 3.5.3 Old cats never die............................. 72 3.5.4 Quantum traversable wormholes..................... 72 3.6 Discussions and future directions........................ 75 3.A Linear responses.................................. 77 vi CONTENTS 3.B An identity.................................... 79 3.C Details of CFT calculation............................ 80 3.C.1 Approximation of identity Virasoro block by conformal transformation 80 3.C.2 Application to W ............................. 84 3.C.3 Explicit expression of A ......................... 85 3.D Full k-dependence in multiple operator species................. 87 3.E Robustness of regenesis.............................. 93 References 99 vii Citations to previously published work Most of this thesis has appeared in print elsewhere. Details for particular chapters are given below. Chapter 2 • Gao, Ping, Daniel Louis Jafferis, and Aron C. Wall. \Traversable wormholes via a double trace deformation." Journal of High Energy Physics 2017.12 (2017): 151. arXiv:1608.05687 Chapter 3 • Gao, Ping, and Hong Liu. \Regenesis and quantum traversable wormholes." arXiv:1810.01444 Electronic preprints (shown in typewriter font) are available on the Internet at the following URL: http://arXiv.org viii Acknowledgments Six-year PhD student life in Harvard is a memorable time, in which I got to know the frontier of physics, started to build up my own research, and had wonderful experiences with many great people, to whom I would like to say \Thank you!" I am deeply grateful to my advisor Prof. Daniel Louis Jafferis. In past six years, he taught me how to think about problems with clear physical intuition. He is brilliant and always has special insight on many seemingly well understood problems. I was often amazed by his ability to capture the essence of problems, which might take me quite a long time of computation to obtain, within just a few lines of simple calculations or some elegant physical argument. Working with him inspired me to try thinking problems in various angles. I believe his insight, taste and enthusiasm towards physics will continue to affect my research in the future. He is a very supportive advisor that he was always optimistic and encouraging me to find a way out whenever I fell into the swamp of complicated calculation and felt frustrated. I specially thank Daniel for guiding me to the project on traversable wormholes, which is the main topic of this thesis. It raises my strong and long-term interest in the interface between quantum gravity, quantum many-body system and quantum information. I would also like to express my gratitude to Prof. Hong Liu. I was impressed by his clear and pedagogically excellent lecture on holographic duality, which helped me understanding this grand topic in a short time. Besides the help in class, I am also grateful for his guidance, stimulating discussions and insightful comments in our collaborations on effective field theory of hydrodynamics and regenesis. He has a strong intuition in finding an elegant and simple physical interpretation behind complicated calculation, which affects my way of thinking on physics. Thanks to my committee members: Prof. Andy Strominger and Prof. Melissa Franklin. They gave me useful feedback on my research process. In particular, I want to single out Andy for his excellent course on black holes that is very beneficial to my understanding on quantum gravity. Moreover, I must express my gratitude to many other professors who taught a course I took or sat in. I have taken Prof. Xi Yin's super well-organzied courses on string theory and CFT, that built up my foundamental knowledge in these areas. I have enjoyed many mathematical courses by Hiro Lee Tanaka, Hector Pasten, Jonathan Mboyo Esole and Prof. Curt McMullen. I am quite impressed by the elegance of mathematics, though it still requires more time for me to gain applicable insight from it. ix CHAPTER 0. ACKNOWLEDGMENTS Thanks to Logan McCarty, Louis Deslauriers, Prof. Daniel Louis Jafferis and Prof. Gerald Gabrielse for giving me opportunities
Load more

Recommended publications
  • Quantum-Corrected Rotating Black Holes and Naked Singularities in (2 + 1) Dimensions
    PHYSICAL REVIEW D 99, 104023 (2019) Quantum-corrected rotating black holes and naked singularities in (2 + 1) dimensions † ‡ Marc Casals,1,2,* Alessandro Fabbri,3, Cristián Martínez,4, and Jorge Zanelli4,§ 1Centro Brasileiro de Pesquisas Físicas (CBPF), Rio de Janeiro, CEP 22290-180, Brazil 2School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland 3Departamento de Física Teórica and IFIC, Universidad de Valencia-CSIC, C. Dr. Moliner 50, 46100 Burjassot, Spain 4Centro de Estudios Científicos (CECs), Arturo Prat 514, Valdivia 5110466, Chile (Received 15 February 2019; published 13 May 2019) We analytically investigate the perturbative effects of a quantum conformally coupled scalar field on rotating (2 þ 1)-dimensional black holes and naked singularities. In both cases we obtain the quantum- backreacted metric analytically. In the black hole case, we explore the quantum corrections on different regions of relevance for a rotating black hole geometry. We find that the quantum effects lead to a growth of both the event horizon and the ergosphere, as well as to a reduction of the angular velocity compared to their corresponding unperturbed values. Quantum corrections also give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the naked singularity case, quantum effects lead to the formation of a horizon that hides the conical defect, thus turning it into a black hole. The fact that these effects occur not only for static but also for spinning geometries makes a strong case for the role of quantum mechanics as a cosmic censor in Nature.
    [Show full text]
  • Advanced Lectures on General Relativity
    Lecture notes prepared for the Solvay Doctoral School on Quantum Field Theory, Strings and Gravity. Lectures given in Brussels, October 2017. Advanced Lectures on General Relativity Lecturing & Proofreading: Geoffrey Compère Typesetting, layout & figures: Adrien Fiorucci Fonds National de la Recherche Scientifique (Belgium) Physique Théorique et Mathématique Université Libre de Bruxelles and International Solvay Institutes Campus Plaine C.P. 231, B-1050 Bruxelles, Belgium Please email any question or correction to: [email protected] Abstract — These lecture notes are intended for starting PhD students in theoretical physics who have a working knowledge of General Relativity. The 4 topics covered are (1) Surface charges as con- served quantities in theories of gravity; (2) Classical and holographic features of three-dimensional Einstein gravity; (3) Asymptotically flat spacetimes in 4 dimensions: BMS group and memory effects; (4) The Kerr black hole: properties at extremality and quasi-normal mode ringing. Each topic starts with historical foundations and points to a few modern research directions. Table of contents 1 Surface charges in Gravitation ................................... 7 1.1 Introduction : general covariance and conserved stress tensor..............7 1.2 Generalized Noether theorem................................. 10 1.2.1 Gauge transformations and trivial currents..................... 10 1.2.2 Lower degree conservation laws........................... 11 1.2.3 Surface charges in generally covariant theories................... 13 1.3 Covariant phase space formalism............................... 14 1.3.1 Field fibration and symplectic structure....................... 14 1.3.2 Noether’s second theorem : an important lemma................. 17 Einstein’s gravity.................................... 18 Einstein-Maxwell electrodynamics.......................... 18 1.3.3 Fundamental theorem of the covariant phase space formalism.......... 20 Cartan’s magic formula...............................
    [Show full text]
  • Static Charged Fluid in (2+ 1)-Dimensions Admitting Conformal
    Accepted for publication in IJMPD STATIC CHARGED FLUID IN (2 + 1)-DIMENSIONS ADMITTING CONFORMAL KILLING VECTORS FAROOK RAHAMAN Department of Mathematics, Jadavpur University, Kolkata 700 032, West Bengal, India [email protected] SAIBAL RAY Department of Physics, Government College of Engineering & Ceramic Technology, Kolkata 700 010, West Bengal, India [email protected] INDRANI KARAR Department of Mathematics, Saroj Mohan Institute of Technology, Guptipara, West Bangal, India [email protected] HAFIZA ISMAT FATIMA Department of Mathematics, The University of Lahore, Lahore, Pakistan [email protected] SAIKAT BHOWMICK Department of Mathematics, Jadavpur University, Kolkata 700 032, West Bengal, India [email protected] arXiv:1211.1228v3 [gr-qc] 24 Feb 2014 GOURAB KUMAR GHOSH Department of Mathematics, Jadavpur University, Kolkata 700 032, West Bengal, India [email protected] Received Day Month Year Revised Day Month Year Communicated by Managing Editor New solutions for (2 + 1)-dimensional Einstein-Maxwell space-time are found for a static spherically symmetric charged fluid distribution with the additional condition of allowing conformal killing vectors (CKV). We discuss physical properties of the fluid parameters. Moreover, it is shown that the model actually represents two structures, namely (i) Gravastar as an alternative of black hole and (ii) Electromagnetic Mass model depending on the nature of the equation state of the fluid. Here the gravitational mass originates from electromagnetic field alone. The solutions are matched with the exterior region of the Ba˜nados-Teitelboim-Zanelli (BTZ) type isotropic static charged black hole as a 1 Accepted for publication in IJMPD 2 consequence of junction conditions. We have shown that the central charge density is dependent on the value of M0, the conserved mass of the BTZ black hole.
    [Show full text]
  • Table of Contents (Print)
    PHYSICAL REVIEW D PERIODICALS For editorial and subscription correspondence, Postmaster send address changes to: please see inside front cover (ISSN: 1550-7998) APS Subscription Services P.O. Box 41 Annapolis Junction, MD 20701 THIRD SERIES, VOLUME 101, NUMBER 10 CONTENTS D15 MAY 2020 The Table of Contents is a total listing of Parts A and B. Part A consists of articles 101501–104021, and Part B articles 104022–109903(E) PART A RAPID COMMUNICATIONS Faithful analytical effective-one-body waveform model for spin-aligned, moderately eccentric, coalescing black hole binaries (7 pages) ........................................................................................... 101501(R) Danilo Chiaramello and Alessandro Nagar ARTICLES Study of the ionization efficiency for nuclear recoils in pure crystals (10 pages) .............................................. 102001 Y. Sarkis, Alexis Aguilar-Arevalo, and Juan Carlos D’Olivo Observation of a potential future sensitivity limitation from ground motion at LIGO Hanford (12 pages) ................ 102002 J. Harms, E. L. Bonilla, M. W. Coughlin, J. Driggers, S. E. Dwyer, D. J. McManus, M. P. Ross, B. J. J. Slagmolen, and K. Venkateswara Efficient gravitational-wave glitch identification from environmental data through machine learning (12 pages) ......... 102003 Robert E. Colgan, K. Rainer Corley, Yenson Lau, Imre Bartos, John N. Wright, Zsuzsa Márka, and Szabolcs Márka Limits on the stochastic gravitational wave background and prospects for single-source detection with GRACE Follow-On (6 pages) ........................................................................................................ 102004 M. P. Ross, C. A. Hagedorn, E. A. Shaw, A. L. Lockwood, B. M. Iritani, J. G. Lee, K. Venkateswara, and J. H. Gundlach Analysis and visualization of the output mode-matching requirements for squeezing in Advanced LIGO and future gravitational wave detectors (14 pages) ............................................................................................
    [Show full text]
  • Holography of the BTZ Black Hole, Inside and out Arxiv:1307.7738V2
    UMD-PP-013-008 Holography of the BTZ Black Hole, Inside and Out Anton de la Fuente and Raman Sundrum Maryland Center for Fundamental Physics Department of Physics University of Maryland College Park, 20782 MD Abstract We propose a 1 + 1 dimensional CFT dual structure for quantum gravity and matter on the extended 2 + 1 dimensional BTZ black hole, realized as a quotient of the Poincaré patch of AdS3. The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincaré patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon.
    [Show full text]
  • Euler Characteris*Cs of Crepant Resolu*Ons of Weierstrass Models
    Euler characteris-cs of crepant resolu-ons of Weierstrass models Jonathan Mboyo Esole Northeastern University Collaborators • Paolo Aluffi • James Fullwood • Ravi Jagadassan • Patrick Jefferson • Monica Kang • Sabrina Pasterski • Julian Salazar • Shu-Heng Shao • Shing-Tung Yau Topology was first a dream of Leibniz “I am s'll not sa'sfied with algebra, in that it yields neither the shortest proofs nor the most beau'ful construcons of geometry. Consequently, in view of this, I consider that we need yet another kind of analysis, geometric or linear, which deals directly with posi'on, as algebra deals with magnitude.” Leibniz’s leDer to Huygens, September 8, 1679. Seven bridges of Königsberg Königsberg is a medieval city on the Pregal river with two big islands on the river and exactly seven bridges connec-ng the islands and the banks. Photo credit: Wikipedia. Seven bridges of Königsberg Ehler introduced the following famous problem to Euler: Is there a route which crosses every bridges once and only once? Euler’s negave solu-on to the problem gave birth to both graph theory and topology. Photo credit: Wikipedia. Euler formula for regular polyhedra Euler also gave us the first topological invariant, the Euler characteris-c. χ = E V + F − E : = number of edges V := number of ver-ces F := number of faces Euler-Poincaré characteris-c Given a smooth manifold M, its Euler-Poincaré characteris-c is a topological invariant given by the alternang sum of Be numbers: χ(M):=β β + β + +( 1)nβ 0 − 1 2 ··· − n βi is the i-th Betti number of M Gauss-Bonnet Theorem The Gauss-Bonnet Theorem expresses the Euler characteris-c Of a manifold by its curvature: KdM=2⇡(M) Z It relates a differen-al geometric invariant with a tological one.
    [Show full text]
  • Conformal Field Theory and Black Hole Physics
    CONFORMAL FIELD THEORY AND BLACK HOLE PHYSICS Steve Sidhu Bachelor of Science, University of Northern British Columbia, 2009 A Thesis Submitted to the School of Graduate Studies of the University of Lethbridge in Partial Fulfilment of the Requirements for the Degree MASTER OF SCIENCE Department of Physics and Astronomy University of Lethbridge LETHBRIDGE, ALBERTA, CANADA c Steve Sidhu, 2012 Dedication To my parents, my sister, and Paige R. Ryan. iii Abstract This thesis reviews the use of 2-dimensional conformal field theory applied to gravity, specifically calculating Bekenstein-Hawking entropy of black holes in (2+1) dimen- sions. A brief review of general relativity, Conformal Field Theory, energy extraction from black holes, and black hole thermodynamics will be given. The Cardy formula, which calculates the entropy of a black hole from the AdS/CFT duality, will be shown to calculate the correct Bekenstein-Hawking entropy of the static and rotating BTZ black holes. The first law of black hole thermodynamics of the static, rotating, and charged-rotating BTZ black holes will be verified. iv Acknowledgements I would like to thank my supervisors Mark Walton and Saurya Das. I would also like to thank Ali Nassar and Ahmed Farag Ali for the many discussions, the Theo- retical Physics Group, and the entire Department of Physics and Astronomy at the University of Lethbridge. v Table of Contents Approval/Signature Page ii Dedication iii Abstract iv Acknowledgements v Table of Contents vi 1 Introduction 1 2 Einstein’s field equations and black hole solutions 7 2.1 Conventions and notations . 7 2.2 Einstein’s field equations .
    [Show full text]
  • Rotating Charged Black String and Three Dimensional Black Holes
    CORE Metadata, citation and similar papers at core.ac.uk Provided by CERN Document Server Rotating Charged Black String and Three Dimensional Black Holes Jos´eP.S.Lemos1 Departamento de Astrof´ısica Observat´orio Nacional – CNPq Rua General Jos´e Cristino 77, 20921, Rio de Janeiro, RJ, Brazil, & Departamento de F´ısica Instituto Superior T´ecnico Av. Rovisco Pais 1, 1096, Lisboa, Portugal Vilson T. Zanchin 2 Departamento de F´ısica-CCNE Universidade Federal de Santa Maria 97119-900 Santa Maria, RS, Brazil 1e-mail:[email protected] 2Present address: Department of Physics, Brown University, Providence, R.I. 02912. e-mail:[email protected] Abstract Einstein-Maxwell equations with a cosmological constant are analyzed in a stationary spacetime admitting an isometry group R×U(1). We find charged rotating black string solutions in a spacetime asymptotically anti-de Sitter in the radial direction. The mass (M), angular momentum (J) and charge (Q) line densities are defined using the Hamiltonian formalism of Brown and York. It is shown through dimensional reduction that M, J and Q are respec- tively the mass, angular momentum and charge of a related three dimensional black hole. The black string solutions are classified according to the charge and angular momentum parameters. The causal structure of each case is studied in detail for different ranges of the parameters and the Penrose dia- grams are shown. There are many similarities between the charged rotating black string and the Kerr-Newman spacetime. The solution has Cauchy and event horizons, ergosphere, timelike singularities, closed timelike curves, and extremal cases.
    [Show full text]
  • From Black Holes to Baby Universes in CGHS Gravity Arxiv:2103.13422V2
    From black holes to baby universes in CGHS gravity Victor Godeta and Charles Marteaub a International Centre for Theoretical Sciences (ICTS-TIFR), Tata Institute of Fundamental Research, Shivakote, Hesaraghatta, Bangalore 560089, India e-mail: [email protected] b Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 0C2, Canada e-mail: [email protected] ABSTRACT. We study CGHS\ gravity, a variant of the matterless Callan-Giddings- Harvey-Strominger model. We show that it describes a universal sector of the near hori- zon perturbations of non-extremal black holes in higher dimensions. In many respects this theory can be viewed as a flat space analog of Jackiw-Teitelboim gravity. The result for the Euclidean path integral implies that CGHS\ is dual to a Gaussian ensemble that we describe in detail. The simplicity of this theory allows us to compute exact quantities such as the quenched free energy and provides a useful playground to study baby universes, averages and factorization. In particular we derive a “wormhole = diagonal” identity. We also give evidence for the existence of a non-perturbative completion in terms of a matrix arXiv:2103.13422v2 [hep-th] 28 Jun 2021 model. Finally, flat wormhole solutions in this model are discussed. 2 1 Introduction3 1.1 Black hole near horizon dynamics . .3 1.2 Euclidean path integral in gravity . .5 1.3 Summary . .7 2 The CGHSd model8 2.1 Review of the model . .8 2.2 Boundary action . .9 2.3 Euclidean path integral . 13 3 Near horizon dynamics of non-extremal black holes 16 3.1 BTZ black hole .
    [Show full text]
  • Spacetime Geometry of a Wormhole Modified BTZ Black Hole
    Spacetime geometry of a wormhole modified BTZ black hole David Sundelin Supervisor Bo Sundborg Stockholm University October 26, 2018 2 Spacetime geometry of a wormhole modified BTZ black hole David Sundelin Abstract The unitarity problem for the BTZ black hole can possibly be solved by a coordinate transformation in which the event horizon is extended to a wormhole. In a model proposed by S.N. Solodukhin, this is done by the addition of a wormhole parameter λ to the BTZ black hole line element. This thesis studies the changes in the spacetime geometry that comes with the addition of such a parameter. The focus of study are geodesic behaviour and possible bound states of waves. Investigating a possible source of the wormhole, the stress-energy tensor ansatz for a perfect fluid is also tested. The thesis concludes that there are notable changes to the spacetime depending on the presence of either a black hole or a wormhole. These changes includes orbital trajectories of geodesics and localized bound states of waves. The changes are most notable for λ > 1 but also detectable for small parameter corrections. The wormhole spacetime can however not be generated by a simple addition of matter in a perfect fluid form. 3 4 Contents 1 Introduction 7 2 Background 9 2.1 General relativity . 9 2.2 Anti-de Sitter spacetime . 10 2.3 Unitarity and the AdS/CFT correspondence . 11 2.4 Wormhole modification of a BTZ black hole . 12 3 Spacetime geometry of a wormhole modified BTZ black hole 14 3.1 Implications for the stress energy tensor .
    [Show full text]
  • The Shape of Inner Space Provides a Vibrant Tour Through the Strange and Wondrous Possibility SPACE INNER
    SCIENCE/MATHEMATICS SHING-TUNG $30.00 US / $36.00 CAN Praise for YAU & and the STEVE NADIS STRING THEORY THE SHAPE OF tring theory—meant to reconcile the INNER SPACE incompatibility of our two most successful GEOMETRY of the UNIVERSE’S theories of physics, general relativity and “The Shape of Inner Space provides a vibrant tour through the strange and wondrous possibility INNER SPACE THE quantum mechanics—holds that the particles that the three spatial dimensions we see may not be the only ones that exist. Told by one of the Sand forces of nature are the result of the vibrations of tiny masters of the subject, the book gives an in-depth account of one of the most exciting HIDDEN DIMENSIONS “strings,” and that we live in a universe of ten dimensions, and controversial developments in modern theoretical physics.” —BRIAN GREENE, Professor of © Susan Towne Gilbert © Susan Towne four of which we can experience, and six that are curled up Mathematics & Physics, Columbia University, SHAPE in elaborate, twisted shapes called Calabi-Yau manifolds. Shing-Tung Yau author of The Fabric of the Cosmos and The Elegant Universe has been a professor of mathematics at Harvard since These spaces are so minuscule we’ll probably never see 1987 and is the current department chair. Yau is the winner “Einstein’s vision of physical laws emerging from the shape of space has been expanded by the higher them directly; nevertheless, the geometry of this secret dimensions of string theory. This vision has transformed not only modern physics, but also modern of the Fields Medal, the National Medal of Science, the realm may hold the key to the most important physical mathematics.
    [Show full text]
  • Arxiv:1608.05687V3 [Hep-Th] 24 Sep 2019 Sdt Ilt Aslt.W Lodsusteipiain O H Ener the T for Quantum Implications to the Related Discuss Description
    Traversable Wormholes via a Double Trace Deformation Ping Gao1, Daniel Louis Jafferis1, Aron C. Wall2 1Center for the Fundamental Laws of Nature, Harvard University, Cambridge, MA, USA 2School of Natural Sciences, Institute for Advanced Study, Princeton, NJ, USA Abstract After turning on an interaction that couples the two boundaries of an eternal BTZ black hole, we find a quantum matter stress tensor with negative average null energy, whose gravitational backreaction renders arXiv:1608.05687v3 [hep-th] 24 Sep 2019 the Einstein-Rosen bridge traversable. Such a traversable wormhole has an interesting interpretation in the context of ER=EPR, which we suggest might be related to quantum teleportation. However, it cannot be used to violate causality. We also discuss the implications for the energy and holographic entropy in the dual CFT description. 1 Contents 1 Introduction 2 2 Modified bulk two-point function 5 3 1-loop stress tensor 7 4 Holographic Energy and Entropy 10 5 Discussion 12 A dUTUU 15 ´ 1 Introduction Traversable wormholes have long been a source of fascination as a method of long distance transportation [36]. However, such configurations require matter that violates the null energy condition, which is believed to apply in physically reasonable classical theories. In quantum field theory, the null energy condition is false, but in many situations there are other no-go theorems that rule out traversable wormholes. In this work we find that adding certain interactions that couple the two boundaries of eternal AdS- Schwarzschild results in a quantum matter stress tensor with negative average null energy, rendering the wormhole traversable after gravitational backreaction.
    [Show full text]