# Perturbations of a rotating black hole in DHOST theories

## TL;DR

This paper analyzes linear perturbations of a rotating black hole in DHOST theories, providing explicit solutions for scalar and tensor perturbations, and discusses potential modifications to gravitational wave signals compared to general relativity.

## Contribution

It introduces a parametrization enabling explicit scalar perturbation solutions and derives a Teukolsky equation with an effective source for tensor perturbations in DHOST theories.

## Key findings

- Scalar perturbation can be explicitly solved for any black hole spin.
- Tensor perturbations follow a Teukolsky equation with a computable source term.
- Potential deviations in gravitational wave signals from general relativity.

## Abstract

We study linear perturbations of a rotating black hole solution that has been recently discovered in degenerate higher-order scalar-tensor (DHOST) theories. We find a parametrization which permits the explicit resolution of the scalar perturbation while the tensor perturbation is obtained as a Teukolsky equation supplemented by an effective source term. The effective source term is related to the black hole hair and can be computed exactly for any value of the black hole spin. We discuss how the perturbations of the geometry and thus the emitted gravitational waves could be modified in comparison with general relativity.