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

TL;DR

This paper develops a semi-classical approach to analyze quantum scalar field backreaction on asymptotically anti-de Sitter black holes, calculating first-order metric corrections and physical properties using analytical approximations.

Contribution

It introduces a method to compute semi-classical backreaction effects on AdS black holes using analytical approximations for the stress-energy tensor.

Findings

First-order corrections to black hole metrics and horizons are obtained.

Temperature profiles of semi-classical black holes show qualitative differences from classical cases.

Corrections to curvature invariants and photon sphere are computed.

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 $\hbar$) 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.