Parametrized quasinormal mode framework for modified Teukolsky equations
Pablo A. Cano, Lodovico Capuano, Nicola Franchini, S. Maenaut, Sebastian H. Völkel
Abstract
Modifications to general relativity lead to effects in the spectrum of quasinormal 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 quasinormal 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.