Quantum Properties of Topological Black Holes

Abstract

We examine quantum properties of topological black holes which are asymptotically anti--de Sitter. First, massless scalar fields and Weyl spinors which propagate in the background of an anti--de Sitter black hole are considered in an exactly soluble two--dimensional toy model. The Boulware--, Unruh--, and Hartle--Hawking vacua are defined. The latter results to coincide with the Unruh vacuum due to the boundary conditions necessary in asymptotically adS spacetimes. We show that the Hartle--Hawking vacuum represents a thermal equilibrium state with the temperature found in the Euclidean formulation. The renormalized stress tensor for this quantum state is well--defined everywhere, for any genus and for all solutions which do not have an inner Cauchy horizon, whereas in this last case it diverges on the inner horizon. The four--dimensional case is finally considered, the equilibrium states are discussed and a luminosity formula for the black hole of any genus is obtained. Since spacelike infinity in anti--de Sitter space acts like a mirror, it is pointed out how this would imply information loss in gravitational collapse. The black hole's mass spectrum according to Bekenstein's view is discussed and compared to that provided by string theory.

31 pages, one additional figure, enlarged discussion of the higher genus case, comment on the mass and new references added

References in corpus (12)

• Black Hole Entropy from Near-Horizon Microstates
• Black holes with unusual topology
• Thermodynamics of (3+1)-dimensional black holes with toroidal or higher genus horizons
• Topological dilaton black holes
• Thermal Fields, Entropy, and Black Holes
• Rotating Topological Black Holes
• Formation of Topological Black holes from Gravitational Collapse
• Entropy of Three-Dimensional Black Holes in String Theory
• Canonical Quantum Statistics of an Isolated Schwarzschild Black Hole with a Spectrum E_n = sigma sqrt{n} E_P
• Gravitational collapse to toroidal, cylindrical and planar black holes
• String Theory Formulation of anti-de Sitter Black Holes
• Black Holes with Multiple Charges and the Correspondence Principle

Cited by in corpus (24)

• Hawking Radiation from AdS Black Holes
• Topological black holes in the dimensionally continued gravity
• Supersymmetry of Anti-de Sitter Black Holes
• The Persistence of the Large Volumes in Black Holes
• New hairy black holes with negative cosmological constant
• Black hole evaporation in Lovelock gravity with diverse dimensions
• Black hole evaporation in Conformal (Weyl) gravity
• Black Hole Evaporation in Hořava-Lifshitz Gravity
• Cold Black Holes in the Harlow-Hayden Approach to Firewalls
• The Quantum Atmosphere of Reissner-Nordström Black Holes
• Hawking Evaporation Time Scale of Topological Black Holes in Anti-de Sitter Spacetime
• Ground and thermal states for the Klein-Gordon field on a massless hyperbolic black hole with applications to the anti-Hawking effect
• New nonabelian solutions in D=4, N=4 gauged supergravity
• Supergravity p-branes revisited: extra parameters, uniqueness, and topological censorship
• A Complementary Third Law for Black Hole Thermodynamics
• Hawking temperature for near-equilibrium black holes
• How Anti-de Sitter Black Holes Reach Thermal Equilibrium
• Black branes in AdS: BPS bounds and asymptotic charges
• Semi-Classical Backreaction on Asymptotically Anti-de Sitter Black Holes
• Vacuum polarization for varying quantum scalar field parameters in Schwarzschild-anti-de Sitter spacetime
• Singularities, geodesics and Green functions in the BTZ black hole
• A scalar invariant and the local geometry of a class of static spacetimes
• Stability of degenerate Cauchy horizons in black hole spacetimes
• Topological Black Holes in Quantum Gravity