High frequency quasi-normal modes for black-holes with generic singularities

TL;DR

This paper calculates high frequency quasi-normal modes for a broad class of spherically symmetric black-holes with generic singularities, revealing an equispaced horizon area spectrum and extending previous results to various black-hole types.

Contribution

It provides a general formula for high frequency QNM of black-holes with arbitrary singularities, linking QNM frequencies to horizon properties and spectrum quantization.

Findings

QNM frequencies proportional to log of a cosine function involving singularity parameters.

Horizon area spectrum is shown to be equispaced for these black-holes.

Results extend to extremal Reissner-Nordström and stringy black-holes.

Abstract

We compute the high frequency quasi-normal modes (QNM) for scalar perturbations of spherically symmetric single horizon black-holes in $(D+2)$-space-time dimensions with generic curvature singularities and having metrics of the form $ds^2 = \eta x^p (dy^2-dx^2) + x^q d\O_D^2$ near the singularity $x=0$. The real part of the QN frequencies is shown to be proportional to $\log \le[ 1 + 2\cos \le(\p \le[ qD -2 \ri]/2 \ri) \ri]$ where the constant of proportionality is equal to the Hawking temperature for non-degenerate black-holes and inverse of horizon radius for degenerate black-holes. Apart from agreeing with the QN frequencies that have been computed earlier, our results imply that the horizon area spectrum for the general spherically symmetric black-holes is equispaced. Applying our results, we also find the QNM frequencies for extremal Reissner-Nordstr\"om and various stringy black-holes.