paper

The physical interpretation of the spectrum of black hole quasinormal modes

arXiv:0711.3145 · doi:10.1103/PhysRevLett.100.141301

Abstract

When a classical black hole is perturbed, its relaxation is governed by a set of quasinormal modes with complex frequencies ω= ω_R+iω_I. We show that this behavior is the same as that of a collection of damped harmonic oscillators whose real frequencies are (ω_R^2+ω_I^2)^{1/2}, rather than simply ω_R. Since, for highly excited modes, ω_I >> ω_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 ΔA=8π\lpl^2, where \lpl is the Planck length (in contrast with the original result ΔA=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.

4 pages, 2 figures; v3: added references and comments. To appear in Phys. Rev. Lett

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