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

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 $d{s}^2=\eta x^p(d{y}^2-d{x}^2)+x^{q}d{\text{O}}_D^2$ near the singularity $x=0$. The real part of the QN frequencies is shown to be proportional to $\log \le [1+2\cos \le (\text{p}\le [qD-2\text{ri}]\mathrm{/}2\text{ri})\text{ri}]$ 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.