On the effective metric of axial black hole perturbations in DHOST gravity
Abstract
We study axial (or odd-parity) perturbations about static and spherically symmetric hairy black hole (BH) solutions in shift-symmetric DHOST (Degenerate Higher-Order Scalar-Tensor) theories. We first extend to the family of DHOST theories the first-order formulation that we recently developed for Horndeski theories. Remarkably, we find that the dynamics of DHOST axial perturbations is equivalent to that of axial perturbations in general relativity (GR) evolving in a, distinct, effective metric. In the particular case of quadratic DHOST theories, this effective metric is derived from the background BH metric via a disformal transformation. We illustrate our general study with three examples of BH solutions. In some so-called stealth solutions, the effective metric is Schwarzschild with a shifted horizon. We also give an example of BH solution for which the effective metric is associated with a naked singularity.
Keywords
Cite
@article{arxiv.2205.07746,
title = {On the effective metric of axial black hole perturbations in DHOST gravity},
author = {David Langlois and Karim Noui and Hugo Roussille},
journal= {arXiv preprint arXiv:2205.07746},
year = {2022}
}
Comments
Version accepted in JCAP