The physical interpretation of the spectrum of black hole quasinormal modes

TL;DR

This paper reinterprets black hole quasinormal modes as damped oscillators, leading to a revised understanding of their spectrum and a new quantization of black hole horizon area that is independent of perturbation spin.

Contribution

It introduces a new physical interpretation of quasinormal modes as damped oscillators and revises the black hole area quantization formula based on this insight.

Findings

Black hole quasinormal modes behave like damped harmonic oscillators.

The horizon area of a Schwarzschild black hole is quantized in units of 8πl_p^2.

The new area quantization is independent of the perturbation's spin.

Abstract

When a classical black hole is perturbed, its relaxation is governed by a set of quasinormal modes with complex frequencies \omega= \omega_R+i\omega_I. We show that this behavior is the same as that of a collection of damped harmonic oscillators whose real frequencies are (\omega_R^2+\omega_I^2)^{1/2}, rather than simply \omega_R. Since, for highly excited modes, \omega_I >> \omega_R, this observation changes drastically the physical understanding of the black hole spectrum, and forces a reexamination of various results in the literature. In particular, adapting a derivation by Hod, we find that the area of the horizon of a Schwarzschild black hole is quantized in units \Delta A=8\pi\lpl^2, where \lpl is the Planck length (in contrast with the original result \Delta A=4\log(3) \lpl^2). The resulting area quantization does not suffer from a number of difficulties of the original proposal; in particular, it is an intrinsic property of the black hole, independent of the spin of the perturbation.