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

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.

Automated summary

We studied linear perturbations about static and spherically symmetric black hole solutions with stealth scalar hair in degenerate higher-order scalar-tensor (DHOST) theories. Master variables were clarified and the quadratic Lagrangian for both odd- and even-parity perturbations was derived. It was found that the even modes are generally plagued by gradient instabilities, or else the perturbations would be strongly coupled.