A Weyl's law for black holes - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

A Weyl's law for black holes

Résumé

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 provide a probe into the effective dimensionality of spacetime and the relevant resonant scales of actual astrophysical black holes, upon the counting of sufficiently many overtones in the observed ringdown signal of binary black hole mergers.

Dates et versions

hal-03921051 , version 1 (03-01-2023)

Identifiants

Citer

José Luis Jaramillo, Rodrigo P. Macedo, Oscar Meneses-Rojas, Bernard Raffaelli, Lamis Al Sheikh. A Weyl's law for black holes. 2023. ⟨hal-03921051⟩
21 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More