Ringdown spectroscopy of rotating black holes pierced by cosmic strings

Cheung, Mark Ho-Yeuk; Poon, Levi Wing-Hei; Chung, A. K. W.; Li, Tjonnie G. F.

doi:10.1088/1475-7516/2021/02/040

Cited by 6 publications

(1 citation statement)

References 73 publications

(106 reference statements)

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“…of Petrov type I instead of D [60][61][62]). As a result of the modified field equations and the non-GR corrections to BHs in these theories, their QNM spectra can be quite different than that predicted in GR [63][64][65][66][67][68][69][70][71], in principle allowing for new tests with GWs [72][73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88].…”

Section: Introductionmentioning

confidence: 99%

Spectral Method for the Gravitational Perturbations of Black Holes: Schwarzschild Background Case

Chung¹,

Wagle²,

Yunes³

2023

Preprint

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We develop a novel technique through spectral decompositions to study the gravitational perturbations of a black hole, without needing to decouple the linearized field equations into master equations and separate their radial and angular dependence. We first spectrally decompose the metric perturbation in a Legendre and Chebyshev basis for the angular and radial sectors respectively, using input from the asymptotic behavior of the perturbation at spatial infinity and at the black hole event horizon. This spectral decomposition allows us to then transform the linearized Einstein equations (a coupled set of partial differential equations) into a linear matrix equation. By solving the linear matrix equation for its generalized eigenvalues, we can estimate the complex quasinormal frequencies of the fundamental mode and various overtones of the gravitational perturbations simultaneously and to high accuracy. We apply this technique to perturbations of a non-spinning, Schwarzschild black hole in general relativity and find the complex quasinormal frequencies of 2 fundamental modes and their first 2 overtones. We demonstrate that the technique is robust and accurate, in the Schwarzschild case leading to relative fractional errors of ≤ 10 −10 − 10 −8 for the fundamental modes, ≤ 10 −7 − 10 −6 for their first overtones, ≤ 10 −7 − 10 −4 for their second overtones. This method can be applied to any black hole spacetime, irrespective of its Petrov type, making the numerical technique extremely powerful in the study of black hole ringdown in and outside general relativity.

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