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

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 $d{s}^2=\eta x^p(d{y}^2-d{x}^2)+x^{q}d{Ø}_D^2$ 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-Nordström and various stringy black-holes.

10 Pages, Revtex4, References added; Final Version: Minor changes to match version appeared in Class. Quant. Grav. Lett

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• Black hole entropy in Loop Quantum Gravity
• Black hole entropy from Quantum Geometry
• WKB analysis of the Regge-Wheeler equation down in the frequency plane
• Quasinormal modes for single horizon black holes in generic 2-d dilaton gravity
• The universal area spectrum in single-horizon black holes

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