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arXiv · 2304.03055

Axial perturbations of black holes in scalar-tensor gravity: near-horizon behaviour

Karim Noui·Hugo Roussille·David Langlois
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Abstract

We consider axial (or odd-parity) perturbations of non-spinning hairy black holes (BH) in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories, including terms quartic and cubic in second derivatives of the scalar field. We give a new formulation of the effective metric in which axial perturbations propagate as in general relativity. We then introduce a generic parametrization of the effective metric in the vicinity of the background BH horizon. Writing the dynamics of the perturbations in terms of a Schr\"odinger-like operator, we discuss in which cases the operator is (essentially) self-adjoint, thus leading to an unambiguous time evolution, according to the choice of parameters characterizing the near-horizon effective metric. This is in particular useful to investigate the stability of the perturbations. We finally illustrate our general analysis with two examples of BH solutions.

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Karim Noui, Hugo Roussille, David Langlois. 2023-04-06. Axial perturbations of black holes in scalar-tensor gravity: near-horizon behaviour. https://doi.org/10.1088/1475-7516%2F2023%2F11%2F040

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