Non-trivial quantum fluctuations in asymptotically non-flat black-hole space-times

TL;DR

This paper investigates quantum fluctuations in asymptotically non-flat black-hole spacetimes, revealing critical length-scales where gravitational back-reaction becomes significant, with implications for black-hole evaporation.

Contribution

It introduces a semi-classical analysis of scalar field stress-tensor fluctuations in non-flat black-hole backgrounds, identifying conditions for significant back-reaction and mode relevance.

Findings

Critical length-scale for back-reaction identified

Finite relevant modes for certain M/L ranges in SAdS and SdS

Implications for late-stage black-hole evaporation discussed

Abstract

Hawking radiation remains a crucial theoretical prediction of semi-classical gravity and is considered one of the critical tests for a model of quantum gravity. However, Hawking's original derivation used quantum field theory on a fixed background. Efforts have been made to include the spacetime fluctuations arising from the quantization of the dynamical degrees of freedom of gravity itself and study the effects on the Hawking particles. Using semi-classical analysis, we study the effects of quantum fluctuations of scalar field stress-tensors in asymptotic non-flat spherically symmetric black-hole space-times. Using two different approaches, we obtain a critical length-scale from the horizon at which gravitational interactions become large, i.e., when the back reaction to the metric due to the scalar field becomes significant. For 4-D Schwarzschild AdS (SAdS) and Schwarzschild de Sitter (SdS), the number of relevant modes for the back-reaction is finite only for a specific range of values of M/L (where M is the mass of the black-hole, and L is related to the modulus of the cosmological constant). For SAdS (SdS), the number of relevant modes is infinite for M/L $\sim$ 1 (0.2 < M/L < $\frac{1}{3\sqrt{3}}$). We discuss the implications of these results for the late stages of black-hole evaporation.