The physical interpretation of the spectrum of black hole quasinormal modes

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.