Semi-Classical Backreaction on Asymptotically Anti-de Sitter Black Holes

Abstract

We consider a quantum scalar field on the classical background of an asymptotically anti-de Sitter black hole and the backreaction the field's stress-energy tensor induces on the black hole geometry. The backreaction is computed by solving the reduced-order semi-classical Einstein field equations sourced by simple analytical approximations for the renormalized expectation value of the scalar field stress-energy tensor. When the field is massless and conformally coupled, we adopt Page's approximation to the renormalised stress energy tensor while for massive fields, we adopt a modified version of the DeWitt-Schwinger approximation. The latter approximation must be modified so that it possesses the correct renormalization freedom required to ensure the semi-classical equations are consistent. Equipped with these approximations, the reduced-order field equations are easily integrated and the first-order (in $\hslash$) corrections to the metric are obtained. We also compute the corrections to the black hole event horizon, surface gravity and minimum temperature as well as corrections to the photon sphere and quadratic curvature invariants. We pay particular attention to the temperature profiles of the semi-classical black holes compared with their classical counterparts, pointing out some interesting qualitative features produced by the backreaction. These results ought to provide reasonable approximations to the first-order (one-loop) quantum backreaction on the geometry of asymptotically anti-de Sitter black holes when the exact numerical stress-energy tensor sources the semi-classical equations.

arXiv comment25 pages, 4 figures. Significant edits to Section IV including the addition of two new subsections. Accepted for publication in Physical Review D

References in corpus (36)

• Formation and evaporation of non-singular black holes
• Quasinormal Modes of AdS Black Holes and the Approach to Thermal Equilibrium
• Black Hole Evaporation without Information Loss
• Quasi-Normal Modes of Schwarzschild Anti-De Sitter Black Holes: Electromagnetic and Gravitational Perturbations
• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• Black hole evaporation: A paradigm
• Black hole fireworks: quantum-gravity effects outside the horizon spark black to white hole tunneling
• Einstein Equation with Quantum Corrections Reduced to Second Order
• Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
• The geodesic structure of the Schwarzschild Anti-de Sitter black hole
• A Self-consistent Model of the Black Hole Evaporation
• Positivity of Entropy in the Semi-Classical Theory of Black Holes and Radiation
• Versatile method for renormalized stress-energy computation in black-hole spacetimes
• The Semi-Classical Back Reaction to Black Hole Evaporation
• Pragmatic mode-sum regularization method for semiclassical black-hole spacetimes
• Breit-Wigner resonances and the quasinormal modes of anti-de Sitter black holes
• Renormalized stress-energy tensor of an evaporating spinning black hole
• Interior of Black Holes and Information Recovery
• Mode-sum regularization of $⟨{\varphi }^2⟩$ in the angular-splitting method
• Semiclassical zero-temperature corrections to Schwarzschild spacetime and holography
• Irreducible forms for the metric variations of the action terms of sixth-order gravity and approximated stress-energy tensor
• The Absence of Horizon in Black-Hole Formation
• Hadamard renormalized scalar field theory on anti-de Sitter space-time
• Semiclassical charged black holes with a quantized massive scalar field
• Quantum Properties of Topological Black Holes
• A Mode-Sum Prescription for Vacuum Polarization in Odd Dimensions
• A Mode-Sum Prescription for Vacuum Polarization in Even Dimensions
• Vacuum polarization in asymptotically anti-de Sitter black hole geometries
• Vacuum Polarization on the Schwarzschild Metric with a Cosmic String
• Black Hole as a Quantum Field Configuration
• Hadamard Renormalization of the Stress Energy Tensor in a Spherically Symmetric Black Hole Space-Time with an Application to Lukewarm Black Holes
• Hadamard Renormalisation of the Stress Energy Tensor on the Horizons of a Spherically Symmetric Black Hole Space-Time
• Self-forces in arbitrary dimensions
• Foundations of the self-force problem in arbitrary dimensions
• Vacuum polarization on topological black holes
• Vacuum polarization for varying quantum scalar field parameters in Schwarzschild-anti-de Sitter spacetime

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