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Asymptotics of linear differential systems and application to quasi-normal modes of nonrotating black holes

Abstract : The traditional approach to perturbations of nonrotating black holes in General Relativity uses the reformulation of the equations of motion into a radial second-order Schr\"odinger-like equation, whose asymptotic solutions are elementary. Imposing specific boundary conditions at spatial infinity and near the horizon defines, in particular, the quasi-normal modes of black holes. For more complicated equations of motion, as encountered for instance in modified gravity models with different background solutions and/or additional degrees of freedom, such a convenient Schr\"odinger-like reformulation might be unavailable, even in a generalised matricial form. In order to tackle such cases, we present a new approach that analyses directly the first-order differential system in its original form and extracts the asymptotic behaviour of perturbations. As a pedagogical illustration, we apply this treatment to the perturbations of Schwarzschild black holes and then show that the standard quasi-normal modes can be obtained numerically by solving this first-order system with a spectral method. This new approach paves the way for a generic treatment of the asymptotic behaviour of black hole perturbations and the identification of quasi-normal modes in theories of modified gravity.
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https://hal.archives-ouvertes.fr/hal-03197535
Contributor : Inspire Hep <>
Submitted on : Tuesday, April 13, 2021 - 10:14:47 PM
Last modification on : Tuesday, May 4, 2021 - 10:18:21 PM

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David Langlois, Karim Noui, Hugo Roussille. Asymptotics of linear differential systems and application to quasi-normal modes of nonrotating black holes. 2021. ⟨hal-03197535⟩

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