Black holes in the 1/D expansion
|
|
- Shannon Dawson
- 5 years ago
- Views:
Transcription
1 Black holes in the 1/D expansion Roberto Emparan ICREA & UBarcelona w/ Tetsuya Shiromizu, Ryotaku Suzuki, Kentaro Tanabe, Takahiro Tanaka
2 R μν = 0 R μν = Λg μν
3 Black holes are very important objects in GR, but they do not appear in the fundamental formulation of the theory They re non-linear, extended field configurations with complicated dynamics
4 Strings are very important in YM theories, but they do not appear in the fundamental formulation of the theory They re non-linear, extended field configurations with complicated dynamics
5 Strings become fundamental objects in the large N limit of SU(N) YM In this limit, they are still extended objects, but their dynamics simplifies drastically
6 Is there a limit of GR in which Black Hole dynamics simplifies a lot? Yes, the limit of large D any other parameter?
7 Is there a limit in which GR can be formulated with black holes as the fundamental (extended) objects? Maybe, the limit of large D
8 BH in D dimensions ds 2 = 1 r 0 r D 3 dt 2 + dr 2 1 r 0 r D 3 + r2 dω D 2
9 Localization of interactions Large potential gradient: Φ r r 0 r D 3 Φ r0 D/r 0 Hierarchy of scales r 0 D r 0 Φ r r 0 r0 D D r
10 Large-D neat separation bh/background r 0 r 0 /D D = 4 D 4
11 r r 0 D r 0 r D 3 0 Flat space Far region
12 r 0 r D 3 = O 1 r r 0 r 0 D r r 0 r 0 D r r 0 : Near-horizon region
13 Near-horizon geometry ds 2 = 1 r 0 r D 3 dt 2 + dr 2 1 r 0 r D 3 + r2 dω D 2 r r 0 D 3 = cosh 2 ρ t near = D 2r 0 t finite as D
14 Near-horizon geometry 2d string bh ds 2 nh 4r 0 2 D 2 tanh2 ρ dt2 near + dρ 2 + r 2 0 (cosh ρ) 4/D 2 dω D 2 2d dilaton string length l s r 0 D Soda 1993 Grumiller et al 2002 RE+Grumiller+Tanabe 2013
15 Near-horizon universality 2d string bh = near-horizon geometry of all neutral non-extremal bhs rotation = local boost (along horizon) cosmo const = 2d bh mass-shift
16 Does this help understand/solve bh dynamics?
17 Quasinormal modes capture interesting perturbative dynamics: -possible instabilities -hydrodynamic behavior but, w/out a small parameter, these modes are not easily distinguished from other more boring quasinormal modes
18 Large D introduces a generic small parameter It isolates the interesting quasinormal modes from the boring modes
19 The distinction comes from whether the modes are normalizable or non-normalizable in the near-horizon region
20 Boring modes Non-normalizable in near-zone Not decoupled from the far zone High frequency: ω D/r 0 Universal spectrum: only sensitive to bh radius Almost featureless oscillations of a hole in flat space
21 Interesting modes Normalizable in near zone Decoupled from the far zone Low frequency: ω D 0 /r 0 Sensitive to bh geometry beyond the leading order Capture instabilities and hydro Efficient calculation to high orders in 1 D
22 Black hole perturbations Quasinormal modes of Schw-(A)dS bhs Gregory-Laflamme instability Ultraspinning instability All solved analytically
23 Fully non-linear large D
24 Replace bh Surface in background What s the dynamics of this surface? D 4 D
25 Large D Effective Theory Solve near-horizon equations Effective theory for the slow decoupling modes
26 Gradient hierarchy Horizon: ρ D Horizon: z 1 ρ z Σ D 3
27 Static geometry ds 2 = N 2 z dρ2 D 2 + g ΩΩ ρ, z dσ D 3 +g tt ρ, z dt 2 + g zz ρ, z dz 2 ρ z Σ D 3
28 Einstein momentum-constraint in ρ: g tt K = const K = mean curvature of horizon surface ds 2 h = g tt z dt 2 + dz 2 + R 2 z dσ D 3 R(z) embedded in background Σ D 3
29 Large D static black holes: Soap-film equation (redshifted) g tt K = const
30 Some applications
31 Soap bubble in Minkowski = Schw BH g tt K = const R 2 + R 2 = 1 R(z) R z = sin z S D 3 z S D 2
32 Black droplets Black hole at boundary of AdS AdS boundary dual to CFT in BH background z AdS bulk Numerical solution: Figueras+Lucietti+Wiseman
33 Our numerical code zmin ; zmax 0.67; r0.5; NDSolve r' z z r z 1 r z 2 z 2 1 r z 2 1 z 2,r zmin r0,r, z,zmin,zmax
34 Black droplets
35 Non-uniform black strings z R z Numerical solution: Wiseman
36 Non-uniform black strings z R z = R(z) D 1/ D K = const R + R 2 + R = const
37 Non-uniform black strings R z R z = R (z) D z
38 At NLO we find a critical dimension D for black strings (from 2nd order to 1st order) at D = 13 Numerical value D 13.5 E Sorkin 2004
39 We ve also solved for stationary black holes Ultraspinning bifurcations of (single-spin) Myers-Perry black holes at a r + = 3, 5, 7, Numerical (D=8): a r + = 1.77, 2.27, 2.72 Dias et al
40 Limitations 1/D expansion breaks down when z D Highly non-uniform black strings AdS black funnels 1/D 1/D
41 Time evolution Long wavelength, slow evolution t,z D 0 can lead to large gradients, fast evolution t,z D if so, breakdown of expansion
42 Conclusions
43 1/D expansion of GR is very efficient at capturing dynamics of horizons Reformulation of a sector of GR: bhs in terms of surfaces (membrane-like) decoupled from bulk (grav waves)
44 1/D: it works (not obvious beforehand!)
45 End
46 Spherical reduction of Einstein-Hilbert ds 2 nh = 4r 0 2 D 2 g 2 μν dx μ dx ν + r 2 0 e 4Φ x D 2 2 dω D 2 g μν 2 (x), Φ x I = d 2 x ge 2Φ R + 4 D 3 D 2 Φ 2 + D 3 D 2 4Φ (D 2) 2 e r 0 2d dilaton gravity
47 Spherical reduction of Einstein-Hilbert ds 2 nh = 4r 0 2 D 2 g 2 μν dx μ dx ν + r 2 0 e 4Φ x D 2 2 dω D 2 D Soda, Grumiller et al I d 2 x ge 2Φ R + 4 Φ 2 + D2 r 0 2 2d string gravity l string 2r 0 D
48 BH perturbations: How accurate? Small expansion parameter: 1 D 3 not quite good for D = 4 But it seems to be 1 2(D 3) not so bad in D = 4, if we can compute to higher order (in AdS: 1 2(D 1) )
49 BH perturbations: How accurate? Small expansion parameter: 1 D 3 not quite good for D = 4 But it seems to be 1 2(D 3) not so bad in D = 4, if we can compute higher orders (in AdS: 1 2(D 1) )
50 Quite accurate Quasinormal frequency in D = 4 (vector-type) Im ωr 0 4D calculation Large D=4 l (angular momentum) Calculation up to 1 D3 yields 6% accuracy in D = 4 6% = 1 2 D 3 4 D=4
51 Quantum effects? Dimensionful scale: L Planck = Għ 1 D 2 Quantum effects governed by r 0 L Planck
52 If r 0 L Planck D 0 the bh is fully quantum: Entropy 0 Temperature Evaporation lifetime 0 But other scalings are possible
53 Scaling r 0 L Planck with D: how large are the black holes, which quantum effects are finite at large D Finite entropy: r 0 L Planck D 1 2 Finite temperature: r 0 L Planck D Finite energy of Hawking radn: r 0 L Planck D 2
54 Black hole perturbations Given the general master equation, it s a straightforward perturbative analysis Leading order is simple and universal (solving in 2D string bh): static modes ω 1 D D r 0 0 Higher order perturbations are not universal, but organized by simple leading order solution
Black Hole dynamics at large D
Black Hole dynamics at large D Roberto Emparan ICREA & U. Barcelona & YITP Kyoto w/ Kentaro Tanabe, Ryotaku Suzuki Einstein s eqns even in simplest cases encode a vast amount of physics Black holes colliding,
More informationRotating Charged Black Holes in D>4
Rotating Charged Black Holes in D>4 Marco Caldarelli LPT Orsay & CPhT Ecole Polytechnique based on arxiv:1012.4517 with R. Emparan and B. Van Pol Orsay, 19/01/2010 Summary The many scales of higher D black
More informationBlack Holes, Fluids, and their Instabilities. Roberto Emparan ICREA & U. Barcelona
Black Holes, Fluids, and their Instabilities Roberto Emparan ICREA & U. Barcelona Black Holes are like Fluids Black Holes are like Fluids What does this mean? What is it good for? Black Holes are like
More informationBlack hole instabilities and violation of the weak cosmic censorship in higher dimensions
Black hole instabilities and violation of the weak cosmic censorship in higher dimensions Pau Figueras School of Mathematical Sciences, Queen Mary University of London w/ Markus Kunesch, Luis Lehner and
More informationBlack holes & Blackfolds in Higher Dimensions
Black holes & Blackfolds in Higher Dimensions Roberto Emparan ICREA & U. Barcelona Based on RE, T. Harmark, V. Niarchos, N. Obers to appear Out today! 0902.0427 Why study D>4 gravity? Main motivation (at
More informationκ = f (r 0 ) k µ µ k ν = κk ν (5)
1. Horizon regularity and surface gravity Consider a static, spherically symmetric metric of the form where f(r) vanishes at r = r 0 linearly, and g(r 0 ) 0. Show that near r = r 0 the metric is approximately
More informationThe Role of Black Holes in the AdS/CFT Correspondence
The Role of Black Holes in the AdS/CFT Correspondence Mario Flory 23.07.2013 Mario Flory BHs in AdS/CFT 1 / 30 GR and BHs Part I: General Relativity and Black Holes Einstein Field Equations Lightcones
More informationOn Black Hole Structures in Scalar-Tensor Theories of Gravity
On Black Hole Structures in Scalar-Tensor Theories of Gravity III Amazonian Symposium on Physics, Belém, 2015 Black holes in General Relativity The types There are essentially four kind of black hole solutions
More informationEntanglement and the Bekenstein-Hawking entropy
Entanglement and the Bekenstein-Hawking entropy Eugenio Bianchi relativity.phys.lsu.edu/ilqgs International Loop Quantum Gravity Seminar Black hole entropy Bekenstein-Hawking 1974 Process: matter falling
More informationBlack Holes in Higher-Derivative Gravity. Classical and Quantum Black Holes
Black Holes in Higher-Derivative Gravity Classical and Quantum Black Holes LMPT, Tours May 30th, 2016 Work with Hong Lü, Alun Perkins, Kelly Stelle Phys. Rev. Lett. 114 (2015) 17, 171601 Introduction Black
More informationIntroduction to AdS/CFT
Introduction to AdS/CFT Who? From? Where? When? Nina Miekley University of Würzburg Young Scientists Workshop 2017 July 17, 2017 (Figure by Stan Brodsky) Intuitive motivation What is meant by holography?
More informationAdS/CFT Correspondence and Entanglement Entropy
AdS/CFT Correspondence and Entanglement Entropy Tadashi Takayanagi (Kyoto U.) Based on hep-th/0603001 [Phys.Rev.Lett.96(2006)181602] hep-th/0605073 [JHEP 0608(2006)045] with Shinsei Ryu (KITP) hep-th/0608213
More informationQuark-gluon plasma from AdS/CFT Correspondence
Quark-gluon plasma from AdS/CFT Correspondence Yi-Ming Zhong Graduate Seminar Department of physics and Astronomy SUNY Stony Brook November 1st, 2010 Yi-Ming Zhong (SUNY Stony Brook) QGP from AdS/CFT Correspondence
More informationON THE BLACK HOLE SPECIES
Paris ON THE BLACK HOLE SPECIES (by means of natural selection) Maria J. Rodriguez 16.07.09 Dumitru Astefanesei and MJR ( to appear) Marco Calderelli, Roberto Emparan and MJR ( 0806.1954 [hep-th] ) Henriette
More informationHigher-dimensional Black Holes. Roberto Emparan ICREA & U. Barcelona
Higher-dimensional Black Holes Roberto Emparan ICREA & U. Barcelona Motivation: GR as a tool Most basic set up: vacuum GR R µν =0 only one parameter for tuning: D Motivation: GR as a tool Most basic set
More informationGravitational waves, solitons, and causality in modified gravity
Gravitational waves, solitons, and causality in modified gravity Arthur Suvorov University of Melbourne December 14, 2017 1 of 14 General ideas of causality Causality as a hand wave Two events are causally
More informationBlack Holes in Four and More Dimensions
Black Holes in Four and More Dimensions Jutta Kunz Institute of Physics CvO University Oldenburg International Workshop on In-Medium Effects in Hadronic and Partonic Systems Obergurgl, Austria, February
More informationGravity in the Braneworld and
Gravity in the Braneworld and the AdS/CFT Correspondence Takahiro TANAKA Department of Physics, Kyoto University, Kyoto 606-8502, Japan October 18, 2004 Abstract We discuss gravitational interaction realized
More informationD. f(r) gravity. φ = 1 + f R (R). (48)
5 D. f(r) gravity f(r) gravity is the first modified gravity model proposed as an alternative explanation for the accelerated expansion of the Universe [9]. We write the gravitational action as S = d 4
More informationThe Uses of Ricci Flow. Matthew Headrick Stanford University
The Uses of Ricci Flow Matthew Headrick Stanford University String theory enjoys a rich interplay between 2-dimensional quantum field theory gravity and geometry The most direct connection is through two-dimensional
More informationViscosity Correlators in Improved Holographic QCD
Bielefeld University October 18, 2012 based on K. Kajantie, M.K., M. Vepsäläinen, A. Vuorinen, arxiv:1104.5352[hep-ph]. K. Kajantie, M.K., A. Vuorinen, to be published. 1 Motivation 2 Improved Holographics
More informationKerr black hole and rotating wormhole
Kerr Fest (Christchurch, August 26-28, 2004) Kerr black hole and rotating wormhole Sung-Won Kim(Ewha Womans Univ.) August 27, 2004 INTRODUCTION STATIC WORMHOLE ROTATING WORMHOLE KERR METRIC SUMMARY AND
More informationBlack Hole Formation in Randall-Sundrum II Braneworlds
Black Hole Formation in Randall-Sundrum II Braneworlds Matt Choptuik CIFAR Cosmology & Gravity Program Dept of Physics & Astronomy, UBC Workshop on Numerical and Mathematical Relativity Oppurg, DE September
More informationDilatonic Black Saturn
Dilatonic Black Saturn Saskia Grunau Carl von Ossietzky Universität Oldenburg 7.5.2014 Introduction In higher dimensions black holes can have various forms: Black rings Black di-rings Black saturns...
More informationDynamics of heavy quarks in charged N = 4 SYM plasma
Dynamics of heavy quarks in charged N = 4 SYM plasma Aleksi Vuorinen University of Washington, Seattle & Technical University of Vienna C. Herzog and AV, arxiv:0708:0609 [hep-th] Outline N = 4 SYM and
More informationBlack Holes. Jan Gutowski. King s College London
Black Holes Jan Gutowski King s College London A Very Brief History John Michell and Pierre Simon de Laplace calculated (1784, 1796) that light emitted radially from a sphere of radius R and mass M would
More informationTowards new relativistic hydrodynamcis from AdS/CFT
Towards new relativistic hydrodynamcis from AdS/CFT Michael Lublinsky Stony Brook with Edward Shuryak QGP is Deconfined QGP is strongly coupled (sqgp) behaves almost like a perfect liquid (Navier-Stokes
More informationBlack Hole fusion in the extreme mass-ratio limit
Black Hole fusion in the extreme mass-ratio limit Roberto Emparan ICREA & UBarcelona YKIS2018a Symposium YITP Kyoto 20 Feb 2018 Work with Marina Martínez arxiv:1603.00712 and with Marina Martínez & Miguel
More informationarxiv: v2 [hep-th] 1 Mar 2016
KEK-TH-1867 Black rings at large D Kentaro Tanabe arxiv:1510.02200v2 [hep-th 1 Mar 2016 Theory Center, Institute of Particles and Nuclear Studies, KEK, Tsukuba, Ibaraki, 305-0801, Japan ktanabe@post.kek.jp
More informationOn Complexity Growth for F (R) and Critical Gravity
On Complexity Growth for F (R) and Critical Gravity Mohammad Hassan Vahidinia Institute for Research in Fundamental Sciences (IPM), Iran Based on: Mohsen Alishahiha, Amin Faraji Astaneh, Ali Naseh, Mohammad
More informationBlack holes and the leaking faucet in your bathroom
Black holes and the leaking faucet in your bathroom Nicolas Vasset Journal club May 5th, 2011 Nicolas Vasset (Basel) Black holes and leaking faucets 05/11 1 / 17 Based on the following articles [Lehner
More informationarxiv: v2 [hep-th] 19 Sep 2018
Rotating black holes and black bars at large D Tomás Andrade a, Roberto Emparan a,b, David Licht a arxiv:1807.01131v [hep-th] 19 Sep 018 a Departament de Física Quàntica i Astrofísica, Institut de Ciències
More informationHolography and (Lorentzian) black holes
Holography and (Lorentzian) black holes Simon Ross Centre for Particle Theory The State of the Universe, Cambridge, January 2012 Simon Ross (Durham) Holography and black holes Cambridge 7 January 2012
More informationBlack hole thermodynamics
Black hole thermodynamics Daniel Grumiller Institute for Theoretical Physics Vienna University of Technology Spring workshop/kosmologietag, Bielefeld, May 2014 with R. McNees and J. Salzer: 1402.5127 Main
More informationLarge D Black Hole Membrane Dynamics
Large D Black Hole Membrane Dynamics Parthajit Biswas NISER Bhubaneswar February 11, 2018 Parthajit Biswas Large D Black Hole Membrane Dynamics 1 / 26 References The talk is mainly based on S. Bhattacharyya,
More informationIntroduction to AdS/CFT
Introduction to AdS/CFT D-branes Type IIA string theory: Dp-branes p even (0,2,4,6,8) Type IIB string theory: Dp-branes p odd (1,3,5,7,9) 10D Type IIB two parallel D3-branes low-energy effective description:
More informationProbing Universality in AdS/CFT
1 / 24 Probing Universality in AdS/CFT Adam Ritz University of Victoria with P. Kovtun [0801.2785, 0806.0110] and J. Ward [0811.4195] Shifmania workshop Minneapolis May 2009 2 / 24 Happy Birthday Misha!
More informationJason Doukas Yukawa Institute For Theoretical Physics Kyoto University
1/32 MYERS-PERRY BLACK HOLES: BEYOND THE SINGLE ROTATION CASE Jason Doukas Yukawa Institute For Theoretical Physics Kyoto University Lunch meeting FEB 02, 2011 2/32 Contents 1. Introduction. 1.1 Myers
More informationHolographic Entanglement and Interaction
Holographic Entanglement and Interaction Shigenori Seki RINS, Hanyang University and Institut des Hautes Études Scientifiques Intrication holographique et interaction à l IHES le 30 janvier 2014 1 Contents
More informationTOPIC V BLACK HOLES IN STRING THEORY
TOPIC V BLACK HOLES IN STRING THEORY Lecture notes Making black holes How should we make a black hole in string theory? A black hole forms when a large amount of mass is collected together. In classical
More information8.821 F2008 Lecture 12: Boundary of AdS; Poincaré patch; wave equation in AdS
8.821 F2008 Lecture 12: Boundary of AdS; Poincaré patch; wave equation in AdS Lecturer: McGreevy Scribe: Francesco D Eramo October 16, 2008 Today: 1. the boundary of AdS 2. Poincaré patch 3. motivate boundary
More informationNon-relativistic holography
University of Amsterdam AdS/CMT, Imperial College, January 2011 Why non-relativistic holography? Gauge/gravity dualities have become an important new tool in extracting strong coupling physics. The best
More informationGauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger. Julius-Maximilians-Universität Würzburg
Gauge/Gravity Duality: Applications to Condensed Matter Physics. Johanna Erdmenger Julius-Maximilians-Universität Würzburg 1 New Gauge/Gravity Duality group at Würzburg University Permanent members 2 Gauge/Gravity
More information8.821 String Theory Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.81 String Theory Fall 008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8.81 F008 Lecture 1: Boundary of AdS;
More informationBlack holes, Holography and Thermodynamics of Gauge Theories
Black holes, Holography and Thermodynamics of Gauge Theories N. Tetradis University of Athens Duality between a five-dimensional AdS-Schwarzschild geometry and a four-dimensional thermalized, strongly
More informationQuantum Fields in Curved Spacetime
Quantum Fields in Curved Spacetime Lecture 3 Finn Larsen Michigan Center for Theoretical Physics Yerevan, August 22, 2016. Recap AdS 3 is an instructive application of quantum fields in curved space. The
More informationHolographic relations at finite radius
Mathematical Sciences and research centre, Southampton June 11, 2018 RESEAR ENT Introduction The original example of holography in string theory is the famous AdS/FT conjecture of Maldacena: - String theory
More informationDynamics, phase transitions and holography
Dynamics, phase transitions and holography Jakub Jankowski with R. A. Janik, H. Soltanpanahi Phys. Rev. Lett. 119, no. 26, 261601 (2017) Faculty of Physics, University of Warsaw Phase structure at strong
More informationThe abundant richness of Einstein-Yang-Mills
The abundant richness of Einstein-Yang-Mills Elizabeth Winstanley Thanks to my collaborators: Jason Baxter, Marc Helbling, Eugen Radu and Olivier Sarbach Astro-Particle Theory and Cosmology Group, Department
More informationHolographic transport with random-field disorder. Andrew Lucas
Holographic transport with random-field disorder Andrew Lucas Harvard Physics Quantum Field Theory, String Theory and Condensed Matter Physics: Orthodox Academy of Crete September 1, 2014 Collaborators
More informationBoost-invariant dynamics near and far from equilibrium physics and AdS/CFT.
Boost-invariant dynamics near and far from equilibrium physics and AdS/CFT. Micha l P. Heller michal.heller@uj.edu.pl Department of Theory of Complex Systems Institute of Physics, Jagiellonian University
More informationGravity, Strings and Branes
Gravity, Strings and Branes Joaquim Gomis International Francqui Chair Inaugural Lecture Leuven, 11 February 2005 Fundamental Forces Strong Weak Electromagnetism QCD Electroweak SM Gravity Standard Model
More informationEinstein Toolkit Workshop. Joshua Faber Apr
Einstein Toolkit Workshop Joshua Faber Apr 05 2012 Outline Space, time, and special relativity The metric tensor and geometry Curvature Geodesics Einstein s equations The Stress-energy tensor 3+1 formalisms
More informationTHE 2D ANALOGUE OF THE REISSNER-NORDSTROM SOLUTION. S. Monni and M. Cadoni ABSTRACT
INFNCA-TH9618 September 1996 THE 2D ANALOGUE OF THE REISSNER-NORDSTROM SOLUTION S. Monni and M. Cadoni Dipartimento di Scienze Fisiche, Università di Cagliari, Via Ospedale 72, I-09100 Cagliari, Italy.
More informationTHE ROLE OF BLACK HOLES IN THE ADS/CFT CORRESPONDENCE
THE ROLE OF BLACK HOLES IN THE ADS/CFT CORRESPONDENCE Jakob Gath Submitted in partial fulfilment of the requirements for the degree of Master of Science of the Imperial College London Imperial College
More informationGravity, Strings and Branes
Gravity, Strings and Branes Joaquim Gomis Universitat Barcelona Miami, 23 April 2009 Fundamental Forces Strong Weak Electromagnetism QCD Electroweak SM Gravity Standard Model Basic building blocks, quarks,
More informationA Holographic Description of Black Hole Singularities. Gary Horowitz UC Santa Barbara
A Holographic Description of Black Hole Singularities Gary Horowitz UC Santa Barbara Global event horizons do not exist in quantum gravity: String theory predicts that quantum gravity is holographic:
More informationStructure of black holes in theories beyond general relativity
Structure of black holes in theories beyond general relativity Weiming Wayne Zhao LIGO SURF Project Caltech TAPIR August 18, 2016 Wayne Zhao (LIGO SURF) Structure of BHs beyond GR August 18, 2016 1 / 16
More informationThe nonlinear dynamical stability of infrared modifications of gravity
The nonlinear dynamical stability of infrared modifications of gravity Aug 2014 In collaboration with Richard Brito, Vitor Cardoso and Matthew Johnson Why Study Modifications to Gravity? General relativity
More informationEntropy of Quasiblack holes and entropy of black holes in membrane approach
Entropy of Quasiblack holes and entropy of black holes in membrane approach José P. S. Lemos Centro Multidisciplinar de Astrofísica, CENTRA, Lisbon, Portugal Oleg B. Zaslavskii Department of Physics and
More informationPAPER 71 COSMOLOGY. Attempt THREE questions There are seven questions in total The questions carry equal weight
MATHEMATICAL TRIPOS Part III Friday 31 May 00 9 to 1 PAPER 71 COSMOLOGY Attempt THREE questions There are seven questions in total The questions carry equal weight You may make free use of the information
More informationarxiv:gr-qc/ v2 18 Feb 2003
arxiv:gr-qc/0205129v2 18 Feb 2003 BULK SHAPE OF BRANE-WORLD BLACK HOLES ROBERTO CASADIO Dipartimento di Fisica, Università di Bologna and I.N.F.N., Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy
More informationCausality, hyperbolicity, and shock formation in Lovelock theories
Causality, hyperbolicity, and shock formation in Lovelock theories Harvey Reall DAMTP, Cambridge University HSR, N. Tanahashi and B. Way, arxiv:1406.3379, 1409.3874 G. Papallo, HSR arxiv:1508.05303 Lovelock
More information8.821 String Theory Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.821 String Theory Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. 8.821 F2008 Lecture 03: The decoupling
More informationA5682: Introduction to Cosmology Course Notes. 2. General Relativity
2. General Relativity Reading: Chapter 3 (sections 3.1 and 3.2) Special Relativity Postulates of theory: 1. There is no state of absolute rest. 2. The speed of light in vacuum is constant, independent
More informationAstronomy 421. Lecture 24: Black Holes
Astronomy 421 Lecture 24: Black Holes 1 Outline General Relativity Equivalence Principle and its Consequences The Schwarzschild Metric The Kerr Metric for rotating black holes Black holes Black hole candidates
More information9 Symmetries of AdS 3
9 Symmetries of AdS 3 This section consists entirely of exercises. If you are not doing the exercises, then read through them anyway, since this material will be used later in the course. The main goal
More informationAn Introduction to AdS/CFT Correspondence
An Introduction to AdS/CFT Correspondence Dam Thanh Son Institute for Nuclear Theory, University of Washington An Introduction to AdS/CFT Correspondence p.1/32 Plan of of this talk AdS/CFT correspondence
More informationHolography for 3D Einstein gravity. with a conformal scalar field
Holography for 3D Einstein gravity with a conformal scalar field Farhang Loran Department of Physics, Isfahan University of Technology, Isfahan 84156-83111, Iran. Abstract: We review AdS 3 /CFT 2 correspondence
More informationQFT Corrections to Black Holes
Dedicated to the memory of Iaonnis Bakas QFT Corrections to Black Holes Hessamaddin Arfaei In collaboratin with J. Abedi, A. Bedroya, M. N. Kuhani, M. A. Rasulian and K. S. Vaziri Sharif University of
More informationGlueballs at finite temperature from AdS/QCD
Light-Cone 2009: Relativistic Hadronic and Particle Physics Instituto de Física Universidade Federal do Rio de Janeiro Glueballs at finite temperature from AdS/QCD Alex S. Miranda Work done in collaboration
More informationModelling the evolution of small black holes
Modelling the evolution of small black holes Elizabeth Winstanley Astro-Particle Theory and Cosmology Group School of Mathematics and Statistics University of Sheffield United Kingdom Thanks to STFC UK
More informationAsymptotic Quasinormal Frequencies for d Dimensional Black Holes
Asymptotic Quasinormal Frequencies for d Dimensional Black Holes José Natário (Instituto Superior Técnico, Lisbon) Based on hep-th/0411267 with Ricardo Schiappa Oxford, February 2009 Outline What exactly
More informationStability of Black Holes and Black Branes. Robert M. Wald with Stefan Hollands arxiv:
Stability of Black Holes and Black Branes Robert M. Wald with Stefan Hollands arxiv:1201.0463 Stability It is of considerable interest to determine the linear stablity of black holes in (D-dimensional)
More informationThemodynamics at strong coupling from Holographic QCD
Themodynamics at strong coupling from Holographic QCD p. 1 Themodynamics at strong coupling from Holographic QCD Francesco Nitti APC, U. Paris VII Excited QCD Les Houches, February 23 2011 Work with E.
More informationA Solvable Irrelevant
A Solvable Irrelevant Deformation of AdS $ / CFT * A. Giveon, N. Itzhaki, DK arxiv: 1701.05576 + to appear Strings 2017, Tel Aviv Introduction QFT is usually thought of as an RG flow connecting a UV fixed
More informationEinstein-Maxwell-Chern-Simons Black Holes
.. Einstein-Maxwell-Chern-Simons Black Holes Jutta Kunz Institute of Physics CvO University Oldenburg 3rd Karl Schwarzschild Meeting Gravity and the Gauge/Gravity Correspondence Frankfurt, July 2017 Jutta
More informationLecturer: Bengt E W Nilsson
9 3 19 Lecturer: Bengt E W Nilsson Last time: Relativistic physics in any dimension. Light-cone coordinates, light-cone stuff. Extra dimensions compact extra dimensions (here we talked about fundamental
More informationYun Soo Myung Inje University
On the Lifshitz black holes Yun Soo Myung Inje University in collaboration with T. Moon Contents 1. Introduction. Transition between Lifshitz black holes and other configurations 3. Quasinormal modes and
More informationInstability of extreme black holes
Instability of extreme black holes James Lucietti University of Edinburgh EMPG seminar, 31 Oct 2012 Based on: J.L., H. Reall arxiv:1208.1437 Extreme black holes Extreme black holes do not emit Hawking
More informationEffective temperature for black holes
Effective temperature for black holes Christian Corda May 31, 2011 Institute for Theoretical Physics and Mathematics Einstein-Galilei, Via Santa Gonda 14, 59100 Prato, Italy E-mail addresses: cordac.galilei@gmail.com
More informationAdS/CFT and Second Order Viscous Hydrodynamics
AdS/CFT and Second Order Viscous Hydrodynamics Micha l P. Heller Institute of Physics Jagiellonian University, Cracow Cracow School of Theoretical Physics XLVII Course Zakopane, 20.06.2007 Based on [hep-th/0703243]
More informationProblem 1, Lorentz transformations of electric and magnetic
Problem 1, Lorentz transformations of electric and magnetic fields We have that where, F µν = F µ ν = L µ µ Lν ν F µν, 0 B 3 B 2 ie 1 B 3 0 B 1 ie 2 B 2 B 1 0 ie 3 ie 2 ie 2 ie 3 0. Note that we use the
More informationGeneral Relativity ASTR 2110 Sarazin. Einstein s Equation
General Relativity ASTR 2110 Sarazin Einstein s Equation Curvature of Spacetime 1. Principle of Equvalence: gravity acceleration locally 2. Acceleration curved path in spacetime In gravitational field,
More informationCAUSAL WEDGES in AdS/CFT
CUSL WEDGES in ds/cft Veronika Hubeny Durham University Gauge/Gravity Duality 2013 Max Planck Institute for Physics, 29 July 2013 to 2 ugust 2013 Based on: VH & M.Rangamani: 1204.1698, VH, M.Rangamani,
More informationSpiky strings, light-like Wilson loops and a pp-wave anomaly
Spiky strings, light-like Wilson loops and a pp-wave anomaly M. Kruczenski Purdue University Based on: arxiv:080.039 A. Tseytlin, M.K. arxiv:0804.3438 R. Ishizeki, A. Tirziu, M.K. Summary Introduction
More informationWhat happens at the horizon of an extreme black hole?
What happens at the horizon of an extreme black hole? Harvey Reall DAMTP, Cambridge University Lucietti and HSR arxiv:1208.1437 Lucietti, Murata, HSR and Tanahashi arxiv:1212.2557 Murata, HSR and Tanahashi,
More informationRotating Black Holes in Higher Dimensions
Rotating Black Holes in Higher Dimensions Jutta Kunz Institute of Physics CvO University Oldenburg Models of Gravity in Higher Dimensions Bremen, 25.-29. 8. 2008 Jutta Kunz (Universität Oldenburg) Rotating
More informationCosmological constant is a conserved charge
Cosmological constant is a conserved Kamal Hajian Institute for Research in Fundamental Sciences (IPM) In collaboration with Dmitry Chernyavsky (Tomsk Polytechnic U.) arxiv:1710.07904, to appear in Classical
More informationQuantum Entanglement and the Geometry of Spacetime
Quantum Entanglement and the Geometry of Spacetime Matthew Headrick Brandeis University UMass-Boston Physics Colloquium October 26, 2017 It from Qubit Simons Foundation Entropy and area Bekenstein-Hawking
More informationThermalization in a confining gauge theory
15th workshop on non-perturbative QD Paris, 13 June 2018 Thermalization in a confining gauge theory CCTP/ITCP University of Crete APC, Paris 1- Bibliography T. Ishii (Crete), E. Kiritsis (APC+Crete), C.
More informationAn Inverse Mass Expansion for Entanglement Entropy. Free Massive Scalar Field Theory
in Free Massive Scalar Field Theory NCSR Demokritos National Technical University of Athens based on arxiv:1711.02618 [hep-th] in collaboration with Dimitris Katsinis March 28 2018 Entanglement and Entanglement
More informationGravity in lower dimensions
Gravity in lower dimensions Daniel Grumiller Institute for Theoretical Physics Vienna University of Technology Uppsala University, December 2008 Outline Why lower-dimensional gravity? Which 2D theory?
More information21 Holographic Entanglement Entropy
21 Holographic Entanglement Entropy 21.1 The formula We now turn to entanglement entropy in CFTs with a semiclassical holographic dual. That is, we assume the CFT has a large number of degrees of freedom
More informationBose-Einstein graviton condensate in a Schwarzschild black hole
Bose-Einstein graviton condensate in a Schwarzschild black hole Jorge Alfaro, Domènec Espriu and Departament de Física Quàntica i Astrofísica & Institut de Ciències del Cosmos, Universitat de Barcelona
More informationBlack-hole & white-hole horizons for capillary-gravity waves in superfluids
Black-hole & white-hole horizons for capillary-gravity waves in superfluids G. Volovik Helsinki University of Technology & Landau Institute Cosmology COSLAB Particle Particle physics Condensed matter Warwick
More informationcarroll/notes/ has a lot of good notes on GR and links to other pages. General Relativity Philosophy of general
http://pancake.uchicago.edu/ carroll/notes/ has a lot of good notes on GR and links to other pages. General Relativity Philosophy of general relativity. As with any major theory in physics, GR has been
More informationFormation and Evaporation of Regular Black Holes in New 2d Gravity BIRS, 2016
Formation and Evaporation of Regular Black Holes in New 2d Gravity BIRS, 2016 G. Kunstatter University of Winnipeg Based on PRD90,2014 and CQG-102342.R1, 2016 Collaborators: Hideki Maeda (Hokkai-Gakuen
More informationOn the Hawking Wormhole Horizon Entropy
ESI The Erwin Schrödinger International Boltzmanngasse 9 Institute for Mathematical Physics A-1090 Wien, Austria On the Hawking Wormhole Horizon Entropy Hristu Culetu Vienna, Preprint ESI 1760 (2005) December
More informationDon Marolf 7/17/14 UCSB
Don Marolf 7/17/14 UCSB D=4: F = GM 2 /r 2, dimensionless coupling GE 2 /ħc 5 grows with E. Quantum fluctuations are a problem, growing at short distances. Growth must(?) stop somewhere (non trivial fixed
More information