Abstract
Linear perturbations of spherically symmetric spacetimes in general relativity are described by radial wave equations, with potentials that depend on the spin of the perturbing field. In previous work we studied the quasinormal mode spectrum of spacetimes for which the radial potentials are slightly modified from their general relativistic form, writing generic small modifications as a power-series expansion in the radial coordinate. We assumed that the perturbations in the quasinormal frequencies are linear in some perturbative parameter, and that there is no coupling between the perturbation equations. In general, matter fields and modifications to the gravitational field equations lead to coupled wave equations. Here we extend our previous analysis in two important ways: we study second-order corrections in the perturbative parameter, and we address the more complex (and realistic) case of coupled wave equations. We highlight the special nature of coupling-induced corrections when two of the wave equations have degenerate spectra, and we provide a ready-to-use recipe to compute quasinormal modes. We illustrate the power of our parametrization by applying it to various examples, including dynamical Chern-Simons gravity, Horndeski gravity and an effective field theory-inspired model.
Highlights
There are experimental and conceptual reasons to expect that general relativity (GR) and the standard model of particle physics should be modified at some level
We still work under the assumption that the background solution is nonspinning and that the perturbation equations are separable
Gravitational perturbations of the Schwarzschild geometry in GR can be classified by their behavior under parity
Summary
There are experimental and conceptual reasons to expect that general relativity (GR) and the standard model of particle physics should be modified at some level. Astrophysical BHs in GR are remarkably simple, being characterized only by their mass and spin by virtue of the so-called “no-hair theorems” [11,12,13,14,15,16] As such, they are ideal laboratories for precision measurements: any deviation from this simplicity is a potential hint of new physics. We found that corrections to the QNM frequencies are (to leading order) linear in these perturbations, and we computed the coefficients that determine these corrections We extend these results by calculating quadratic corrections in the perturbative potentials, as well as the corrections that arise from coupling power-law perturbative corrections between the scalar, vector, polar (even-parity) and axial (odd-parity) gravitational perturbation equations in GR. We still work under the assumption that the background solution is nonspinning (as shown in Paper I, the formalism can be applied to spinning black holes in the slow-rotation limit [42,59]) and that the perturbation equations are separable
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