Ringdown waves from hairy black holes

TL;DR

This paper investigates how quasinormal-mode frequencies can reveal information about matter sources causing black hole hair, using a perturbative approach relating spectrum shifts to properties of an anisotropic fluid.

Contribution

It introduces formulas linking deviations in QNM spectra to the equation-of-state parameters of anisotropic fluid perturbations around black holes.

Findings

Derived formulas to read off deviations from Schwarzschild or Kerr QNM spectra.

Established a systematic method to compute QNMs for broad classes of hairy black holes.

Linked shifts in ringdown spectrum to photon-orbit frequency and Lyapunov exponent perturbations.

Abstract

We study how quasinormal-mode frequencies may encode information about the effective matter source responsible for black-hole hair. Using the established eikonal correspondence between quasinormal modes and unstable null geodesics, we relate shifts in the ringdown spectrum to perturbations of the photon-orbit frequency and Lyapunov exponent. The black hole hair is treated as an anisotropic fluid perturbatively added to the vacuum black holes (Schwarzschild and Kerr black holes). In particular, we derive formulas which allow one to directly read off deviations from the Schwarzschild or Kerr QNM spectrum in terms of the corresponding equation-of-state parameters of the anisotropic fluid. Under this setting, independent of energy conditions, our formulas offer a systematic method to compute quasi-normal mode frequencies for a broad class of hairy black holes.