Perturbations of a rotating black hole in DHOST theories

We study linear perturbations of a rotating black hole solution that has been recently discovered in the subset of degenerate higher-order scalar?tensor (DHOST) theories where gravity and light propagate with the same speed. 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.