Inside the Horizon with AdS/CFT

Abstract

Using the eternal BTZ black hole as a concrete example, we show how spacelike singularities and horizons can be described in terms of AdS/CFT amplitudes. Our approach is based on analytically continuing amplitudes defined in Euclidean signature. This procedure yields finite Lorentzian amplitudes. The naive divergences associated with the Milne type singularity of BTZ are regulated by an $i\epsilon$ prescription inherent in the analytic continuation and a cancellation between future and past singularities. The boundary description corresponds to a tensor product of two CFTs in an entangled state, as in previous work. We give two bulk descriptions corresponding to two different analytic continuations. In the first, only regions outside the horizon appear explicitly, and so amplitudes are manifestly finite. In the second, regions behind the horizon and on both sides of the singularity appear, thus yielding finite amplitudes for virtual particles propagating through the black hole singularity. This equivalence between descriptions only outside and both inside and outside the horizon is reminiscent of the ideas of black hole complementarity.

31 pages, 6 figures

References in corpus (46)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• The Black Hole in Three Dimensional Space Time
• M Theory As A Matrix Model: A Conjecture
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• AdS3 Black Holes and a Stringy Exclusion Principle
• Massless Black Holes and Conifolds in String Theory
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• Schwinger-Keldysh Propagators from AdS/CFT Correspondence
• Holographic Probes of Anti-de Sitter Spacetimes
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 2: Euclidean Black Hole
• Gauge Theory and the Excision of Repulson Singularities
• A New Cosmological Scenario in String Theory
• The Trouble with de Sitter Space
• Exact Three Dimensional Black Holes in String Theory
• Strings in a Time-Dependent Orbifold
• Holographic Particle Detection
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 3: Correlation Functions
• On structure constants and fusion rules in the $SL(2,\BC)/SU(2)$ WZNW model
• Strings in Time-Dependent Orbifolds
• Instability of Spacelike and Null Orbifold Singularities
• Operator product expansion and factorization in the $H_3^{+}$-WZNW model
• Is There Really a de Sitter/CFT Duality
• A Resolution of the Cosmological Singularity with Orientifolds
• From Big Bang to Big Crunch and Beyond
• Bulk and Boundary Dynamics in BTZ Black Holes
• The geometry of null rotation identifications
• A Space-Time Orbifold: A Toy Model for a Cosmological Singularity
• On the instability of 3d null singularities
• String Propagation in the Presence of Cosmological Singularities
• Miens of The Three Dimensional Black Hole
• On Smooth Time-Dependent Orbifolds and Null Singularities
• A New Approach to String Cosmology
• Vacuum String Field Theory
• Comments on Cosmological Singularities in String Theory
• Quantum Fields in a Big Crunch/Big Bang Spacetime
• Strings in the Extended BTZ Spacetime
• String Theory on AdS Orbifolds
• String theory on three dimensional black holes
• Ghost-free and Modular Invariant Spectra of a String in SL(2,R) and Three Dimensional Black Hole Geometry
• The spectrum of strings on BTZ black holes and spectral flow in the SL(2,R) WZW model
• Precursors see inside black holes
• $O(\tilde{d},\tilde{d})$ Transformations and 3D Black Hole
• Winding strings and AdS_3 black holes

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