Asymptotic Quasinormal Frequencies of d-dimensional Schwarzschild Black Holes

TL;DR

This paper calculates the asymptotic quasinormal frequencies of all gravitational perturbations of d-dimensional Schwarzschild black holes, revealing a universal proportionality to the Hawking temperature and implications for black hole entropy quantization.

Contribution

It provides a comprehensive derivation of the asymptotic quasinormal frequencies for all gravitational perturbations in higher-dimensional Schwarzschild black holes, extending previous results.

Findings

Real part of frequencies proportional to Hawking temperature with log 3 coefficient

Asymptotic frequencies lead to equally spaced entropy spectrum

Implications for eigenvalues in near-horizon conformal algebra

Abstract

We determine the quasinormal frequencies for all gravitational perturbations of the d-dimensional Schwarzschild black hole, in the infinite damping limit. Using the potentials for gravitational perturbations derived recently by Ishibashi and Kodama, we show that in all cases the asymptotic real part of the frequency is proportional to the Hawking temperature with a coefficient of log 3. Via the correspondence principle, this leads directly to an equally spaced entropy spectrum. We comment on the possible implications for the spacing of eigenvalues of the Virasoro generator in the associated near-horizon conformal algebra.