# Perturbations of Stealth Black Holes in DHOST Theories

## TL;DR

This paper examines perturbations around stealth black holes in DHOST theories, revealing that scalar perturbations are strongly coupled and highlighting limitations of these solutions within the effective field theory framework.

## Contribution

It demonstrates that certain DHOST black hole solutions are infinitely strongly coupled due to scalar perturbations, challenging their physical viability.

## Key findings

- Odd-parity tensor perturbations behave like in GR
- Scalar perturbations exhibit singular effective metrics
- Black hole solutions are infinitely strongly coupled

## Abstract

Among the Scalar-Tensor modified theories of gravity, DHOST models could play a special role for dark energy while being consistent with current observations, notably those constraining the speed of gravitational waves. Schwarzschild-de Sitter black holes were shown to be exact solutions of a particular subclass of quadratic DHOST theories, while carrying a nontrivial scalar profile that linearly evolves in time and hence potentially providing exciting new phenomenological windows to explore this model. We investigate the physical perturbations about such black holes and find that the odd-parity tensor perturbations behave in a way indistinguishable to GR. On the other hand, the effective metric for the (even-parity) scalar perturbations is singular, indicating that those exact black hole solutions are infinitely strongly coupled and cannot be trusted within the regime of validity of the DHOST effective field theory. We show how this strong coupling result is generalizable to a whole class of solutions with arbitrary manifolds both for DHOST and Horndeski.