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arXiv · 2407.15947

Parametrized quasi-normal mode framework for modified Teukolsky equations

Pablo A. Cano·Lodovico Capuano·Nicola Franchini·Simon Maenaut·Sebastian H. Völkel
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Abstract

Modifications to general relativity lead to effects in the spectrum of quasi-normal modes of black holes. In this paper, we develop a parametrized formalism to describe deviations from general relativity in the Teukolsky equation, which governs linear perturbations of spinning black holes. We do this by introducing a correction to the effective potential of the Teukolsky equation in the form of a $1/r$ expansion controlled by free parameters. The method assumes that a small deviation in the effective potential induces a small modification in the spectrum of modes and in the angular separation constants. We isolate and compute the universal linear contribution to the quasi-normal mode frequencies and separation constants in a set of coefficients, and test them against known examples in the literature (massive scalar field, Dudley-Finley equation and higher-derivative gravity). We make the coefficients publicly available for relevant overtone, angular momentum and azimuthal numbers of modes and different values of the black hole spin.

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Pablo A. Cano, Lodovico Capuano, Nicola Franchini, Simon Maenaut, Sebastian H. Völkel. 2024-07-22. Parametrized quasi-normal mode framework for modified Teukolsky equations. https://arxiv.org/abs/2407.15947

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