Restoring Unitarity in BTZ Black Hole

Abstract

Whether or not system is unitary can be seen from the way it, if perturbed, relaxes back to equilibrium. The relaxation of semiclassical black hole can be described in terms of correlation function which exponentially decays with time. In the momentum space it is represented by infinite set of complex poles to be identified with the quasi-normal modes. This behavior is in sharp contrast to the relaxation in unitary theory in finite volume: correlation function of the perturbation in this case is quasi-periodic function of time and, in general, is expected to show the Poincaré recurrences. In this paper we demonstrate how restore unitarity in the BTZ black hole, the simplest example of eternal black hole in finite volume. We start with reviewing the relaxation in the semiclassical BTZ black hole and how this relaxation is mirrored in the boundary conformal field theory as suggested by the AdS/CFT correspondence. We analyze the sum over $SL(2,\mathbf{Z})$ images of the BTZ space-time and suggest that it does not produce a quasi-periodic relaxation, as one might have hoped, but results in correlation function which decays by power law. We develop our earlier suggestion and consider a non-semiclassical deformation of the BTZ space-time that has structure of wormhole connecting two asymptotic regions semiclassically separated by horizon. The small deformation parameter $\lambda$ is supposed to have non-perturbative origin to capture the finite N behavior of the boundary theory. The discrete spectrum of perturbation in the modified space-time is computed and is shown to determine the expected unitary behavior: the corresponding time evolution is quasi-periodic with hierarchy of large time scales $\ln 1/\lambda$ and $1/\lambda$ interpreted respectively as the Heisenberg and Poincaré time scales in the system.

23 pages; v3: statement on convergence of (c,d) sum corrected, version to appear in Phys. Rev. D

References in corpus (3)

• Poincare Recurrences and Topological Diversity
• Can Black Hole Relax Unitarily?
• Unitarity, quasi-normal modes and the AdS_3/CFT_2 correspondence

Cited by in corpus (39)

• Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A${}^{\ast }$
• Traversable Wormholes via a Double Trace Deformation
• Time Dependence of Hawking Radiation Entropy
• Conformal Field Theory, (2+1)-Dimensional Gravity, and the BTZ Black Hole
• Wormholes as Black Hole Foils
• The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories
• Fuzzballs and Observations
• Topological Stars, Black holes and Generalized Charged Weyl Solutions
• Punctuated eternal inflation via AdS/CFT
• No Hawking-Page phase transition in three dimensions
• Phase transition between the BTZ black hole and AdS space
• The quantum fate of black hole horizons
• Shadow of a charged black hole with scalar hair
• Static Black Hole and Vacuum Energy: Thin Shell and Incompressible Fluid
• Traversable wormholes in AdS and bounds on information transfer
• On the Near-Horizon Geometry of an Evaporating Black Hole
• Hologram of a pure state black hole
• An Analytic Description of Semi-Classical Black-Hole Geometry
• Gravitoelectromagnetic coupled perturbations and quasinormal modes of a charged black hole with scalar hair
• Black hole complementarity from AdS/CFT
• Two-dimensional Quantum Black Holes, Branes in BTZ and Holography
• Thermodynamics and phase transition of BTZ black hole in a cavity
• Quantum states and their back-reacted geometries in 2d dilaton gravity
• Firewalls as artefacts of inconsistent truncations of quantum geometries
• Thermality from a Rindler quench
• Gravitational Waves, Holography, and Black Hole Microstates
• Space-time structure, asymptotic radiation and information recovery for a quantum hybrid state
• Echoes in the Kerr/CFT correspondence
• Unitarity issue in BTZ black holes
• Quasinormal modes of a charged black hole with scalar hair
• Defining entanglement without tensor factoring: a Euclidean hourglass prescription
• Wormhole-induced effective coupling in SYK chains
• Unitary evolution of perturbations of a two-dimensional black hole
• Finite temperature corrections to black hole quasinormal modes from 2D CFT
• Extractable entanglement from a Euclidean hourglass
• Real-Time Holography and Hybrid WKB for BTZ Wormholes
• Poincare recurrences of Schwarzschild black holes
• Near-extremal Kerr-like ECO in the Kerr/CFT Correspondence in Higher Spin Perturbations
• Aspects of Finite Temperature Quantum Field Theory in a Black Hole Background