Hidden conformal symmetries for black holes in modified gravity

We determine hidden conformal symmetries behind the evolution equations of black hole perturbations in a vector-tensor theory of gravity. Such hidden symmetries are valid everywhere in the exterior region of a spherically symmetric, asymptotically flat black hole geometry. They allow us to factorize second order operators controlling the black hole perturbations into a product of two commuting first order operators. As a consequence, we are able to analytically determine the most general time-dependent solutions for the black hole perturbation equations. We focus on solutions belonging to a highest weight representation of a conformal symmetry, showing that they correspond to quasibound states with an ingoing behavior into the black hole horizon, and exponential decay at spatial infinity. Their time dependence is characterized by purely imaginary frequencies, with imaginary parts separated by integer numbers, as the overtones of quasinormal modes in general relativity.