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

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 Schrödinger-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.

Neutron stars in degenerate higher-order scalar-tensor theories

“…A different class of black holes solutions is the non-rotating Schwarzschild one, which can be obtained from quadratic DHOST theories [74,81,82], but some are disfavoured through a perturbation analysis. Perturbations to such black holes are investigated in [83][84][85][86]. The strong coupling of the solutions in the DHOST theories is discussed [75], together with a solution -adding small corrections (scordatura) to avoid this issue and the implication for the black hole solutions [87].…”