Influence of the back reaction of the Hawking radiation upon black hole quasinormal modes

TL;DR

This paper investigates how Hawking radiation's back reaction affects the quasinormal modes of a BTZ black hole, revealing significant shifts for small black holes that enhance their oscillatory quality.

Contribution

It provides an exact solution for the corrected metric considering quantum effects and quantifies the shift in quasinormal modes due to Hawking radiation back reaction.

Findings

Shift in QNM spectrum proportional to quantum corrections.

Small black holes exhibit increased quality factors.

Quantum corrections negligible for large black holes.

Abstract

We consider the BTZ black hole surrounded by the conformal scalar field. Within general relativity, the resonant \emph{quasinormal} (QN) modes dominate in the response of a black hole to external perturbations. At the same time, the metric of an evaporating black hole is affected by the Hawking radiation. We estimate the shift in the quasinormal spectrum of the BTZ black hole stipulated by the back reaction of the Hawking radiation. For the case of the 2+1 dimensional black hole the corrected (by $\sim \hbar$) metric is an \emph{exact} solution [C.Martines, J.Zanelli (1997)]. In addition, in this case quantum corrections come only from matter fields and no from graviton loops, that is, one can solve the problem of influence of the back reaction upon the QN ringing self-consistently. The dominant contribution to the corrections to the QNMs is simply a shift of $\omega^{2}$ proportional to $-(\frac{\Lambda}{M})^{3/2} (4 L^{2} +M) \hbar$. It is negligible for large black holes but essential for small ones, giving rise to considerable increasing of the quality factor. Thus, the small evaporating black hole is expected to be much better oscillator than a large one.