Charged scalar perturbations on charged black holes in de Rham-Gabadadze-Tolley massive gravity

We explore the quasistationary profile of a massive charged scalar field in a class of charged black holes in de Rham-Gabadadze-Tolley (dRGT) massive gravity. We discuss how the linear term in the metric, which is a unique character of the dRGT massive gravity, affects the structure of the spacetime. Numerical calculations of the quasinormal modes are performed for a charged scalar field in the dRGT black hole background. For an asymptotically de Sitter (dS) black hole, an improved asymptotic iteration method is used to obtain the associated quasinormal frequencies. The unstable modes are found for the ℓ=0 case, and their corresponding real parts satisfy the superradiant condition. For ℓ=2, the results show that all the de Sitter black holes considered here are stable against a small perturbation. For an asymptotically dRGT anti-de Sitter (AdS) black hole, unstable modes are found with the frequency satisfying the superradiant condition. Effects of massive-gravity parameters are discussed. Analytic calculation reveals the unique diffusive nature of quasinormal modes in the massive-gravity model with the linear term. Numerical results confirm the existence of the characteristic diffusive modes in both the dS and AdS cases.