Articles

An analytic approach to quasinormal modes for coupled linear systems

Hui, Lam; Podo, Alessandro; Santoni, Luca; Trincherini, Enrico

Quasinormal modes describe the ringdown of compact objects deformed by small perturbations. In generic theories of gravity that extend General Relativity, the linearized dynamics of these perturbations is described by a system of coupled linear differential equations of second order. We first show, under general assumptions, that such a system can be brought to a Schrödinger-like form. We then devise an analytic approximation scheme to compute the spectrum of quasinormal modes. We validate our approach using a toy model with a controllable mixing parameter ε and showing that the analytic approximation for the fundamental mode agrees with the numerical computation when the approximation is justified. The accuracy of the analytic approximation is at the (sub-) percent level for the real part and at the level of a few percent for the imaginary part, even when ε is of order one. Our approximation scheme can be seen as an extension of the approach of Schutz and Will [1] to the case of coupled systems of equations, although our approach is not phrased in terms of a WKB analysis, and offers a new viewpoint even in the case of a single equation.

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Also Published In

Title
Journal of High Energy Physics
DOI
https://doi.org/10.1007/JHEP03(2023)060

More About This Work

Published Here
July 22, 2024

Notes

Black Holes, Classical Theories of Gravity