Physical Interpretation of the Spectrum of Black Hole Quasinormal Modes

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 damped harmonic oscillators whose real frequencies are (ω_R²+ω_I²)^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=8πl_Pl², in contrast with the original result ΔA=4log⁡(3)l_Pl².