General Relativity and Quantum Cosmology
[Submitted on 9 Nov 2021 (v1), last revised 9 Feb 2022 (this version, v3)]
Title:Gravitational axial perturbations of Schwarzschild-like black holes in dark matter halos
View PDFAbstract: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.
Submission history
From: Tao Zhu [view email][v1] Tue, 9 Nov 2021 06:44:03 UTC (287 KB)
[v2] Tue, 7 Dec 2021 05:59:08 UTC (290 KB)
[v3] Wed, 9 Feb 2022 05:20:23 UTC (290 KB)
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