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Black hole perturbations in modified gravity

Abstract : We study the linear perturbations about nonrotating black holes in the context of degenerate higher-order scalar-tensor (DHOST) theories, using a systematic approach that extracts the asymptotic behaviour of perturbations (at spatial infinity and near the horizon) directly from the first-order radial differential system governing these perturbations. For axial (odd-parity) modes, this provides an alternative to the traditional approach based on a second-order Schrödinger-like equation with an effective potential, which we also discuss for completeness. By contrast, for polar (even-parity) modes, which contain an additional degree of freedom in DHOST theories, a similar generalised second-order Schrödinger-like matricial system does not seem available in general, which leaves only the option of a direct treatment of the four-dimensional first-order differential system. We illustrate our study with two specific types of black hole solutions: "stealth" Schwarzschild black holes, with a non trivial scalar hair, as well as a class of non-stealth black holes whose metric is distinct from Schwarzschild. The knowledge of the asymptotic behaviours of the pertubations enables us to compute numerically quasi-normal modes, as we show explicitly for the non-stealth solutions. Finally, the asymptotic form of the modes also signals some pathologies in the stealth and non-stealth solutions considered here.
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https://hal.archives-ouvertes.fr/hal-03197538
Contributor : Inspire Hep <>
Submitted on : Tuesday, April 13, 2021 - 10:14:57 PM
Last modification on : Tuesday, May 4, 2021 - 10:18:26 PM

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David Langlois, Karim Noui, Hugo Roussille. Black hole perturbations in modified gravity. 2021. ⟨hal-03197538⟩

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