Gravitational axial perturbations of Schwarzschild-like black holes in dark matter halos

TL;DR

This study investigates how dark matter halos with different density profiles influence the axial gravitational perturbations and quasi-normal modes of Schwarzschild-like black holes, affecting gravitational wave signals.

Contribution

It introduces modified Schwarzschild black hole models with dark matter profiles and derives the axial perturbation equations, analyzing their impact on gravitational wave spectra.

Findings

Dark matter halos alter the potential in the perturbation equations.

Quasi-normal mode frequencies are affected by dark matter profiles.

Dark matter influences the gravitational wave spectra emitted by black holes.

Abstract

Gravitational waves emitted by distorted black holes, such as those arising from the coalescence of binary black holes, or a falling compact star into a supermassive black hole, carry not only information about the corresponding spacetime but also information about the environment surrounding the black holes. In this paper, we study the effects of the dark matter halos with three different density profiles on the gravitational axial perturbations of a Schwarzschild-like black hole. For this purpose, we first consider modified Schwarzschild black holes with three different dark matter profiles and derive the equation of motion of the axial perturbations of the modified Schwarzschild metric. It is shown that by ignoring the dark matter perturbations, a Regge-Wheeler-like master equation with a modified potential for the axial perturbation can be obtained explicitly. Then we calculate the complex frequencies of the quasi-normal modes of the Schwarzschild-like black hole in the dark matter halos by applying the sixth-order WKB method. The corresponding gravitational wave spectra with the effects of the dark matter halos have also been discussed.