Black hole perturbations in DHOST theories: Master variables, gradient instability, and strong coupling

TL;DR

This paper analyzes linear perturbations around black holes in DHOST theories, identifying instabilities and strong coupling issues, and discusses potential resolutions for these problems.

Contribution

It derives the quadratic Lagrangian for perturbations in DHOST theories and clarifies master variables, highlighting stability challenges in these models.

Findings

Even modes exhibit gradient instabilities

Perturbations are often strongly coupled

Possible solutions to instabilities are discussed

Abstract

We study linear perturbations about static and spherically symmetric black hole solutions with stealth scalar hair in degenerate higher-order scalar-tensor (DHOST) theories. We clarify master variables and derive the quadratic Lagrangian for both odd- and even-parity perturbations. It is shown that the even modes are in general plagued by gradient instabilities, or otherwise the perturbations would be strongly coupled. Several possible ways out are also discussed.