0000000001001562
AUTHOR
Bernard Raffaelli
A Weyl's law for black holes
We discuss a Weyl's law for the quasi-normal modes of black holes that recovers the structural features of the standard Weyl's law for the eigenvalues of the Laplacian in compact regions. Specifically, the asymptotics of the counting function $N(\omega)$ of quasi-normal modes of $(d+1)$-dimensional black holes follows a power-law $N(\omega)\sim \mathrm{Vol}_d^{\mathrm{eff}}\omega^d$, with $\mathrm{Vol}_d^{\mathrm{eff}}$ an effective volume determined by the light-trapping and decay properties of the black hole geometry. Closed forms are presented for the Schwarzschild black hole and a quasi-normal mode Weyl's law is proposed for generic black holes. As an application, such Weyl's law could …
The overtone level spacing of a black hole quasinormal frequencies: a fingerprint of a local $SL(2,\mathbb{R})$ symmetry
The imaginary part of the quasinormal frequencies spectrum for a static and spherically symmetric black hole is analytically known to be equally spaced, both for the highly damped and the weakly damped families of quasinormal modes. Some interesting attempts have been made in the last twenty years to understand in simple ways this level spacing for the only case of highly damped quasinormal frequencies. Here, we show that the overtone level spacing, for both the highly damped and weakly damped families of quasinormal modes, can simply be understood as a fingerprint of a hidden local $SL(2,\mathbb{R})$ symmetry, near different regions of the black hole spacetime, i.e. the near-horizon and th…