Parametrized quasi-normal mode framework for modified Teukolsky equations

TL;DR

This paper introduces a parametrized framework to describe deviations from general relativity in black hole quasi-normal modes by modifying the Teukolsky equation's effective potential, enabling systematic testing of alternative gravity theories.

Contribution

The paper develops a universal, linear parametrization of deviations in the Teukolsky equation's spectrum, validated against known models, and provides publicly available coefficients for practical use.

Findings

Derived a linear correction to quasi-normal mode frequencies and separation constants.

Validated the formalism against known models like massive scalar fields and higher-derivative gravity.

Provided publicly accessible coefficients for various mode parameters and black hole spins.

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.