We present an exact spherical black hole solution in de Rham, Gabadadze, and Tolley (dRGT) massive gravity for a generic choice of the parameters in the theory, and also discuss the thermodynamical and phase structure of the black hole in both the grand canonical and the canonical ensembles (for the charged case). It turns out that the dRGT black hole solution includes other known solutions to the Einstein field equations, such as the monopole-de SitterSchwarzschild solution with the coefficients of the third and fourth terms in the potential and the graviton mass in massive gravity naturally generates the cosmological constant and the global monopole term. Furthermore, we compute the mass, temperature and entropy of the dRGT black hole, and also perform thermodynamical stability analysis. It turns out that the presence of the graviton mass completely changes the black hole thermodynamics, and it can provide the HawkingPage phase transition which also occurs for the charged black holes. Interestingly, the entropy of a black hole is barely affected and still obeys the standard area law. In particular, our results, in the limit m g → 0, reduced exactly to the results of general relativity.

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

We present a cylindrically symmetric solution, both charged and uncharged, which is known as a black string solution to the nonlinear ghost-free massive gravity found by de Rham, Gabadadze, and Tolley (dRGT). This "dRGT black string" can be thought of as a generalization of the black string solution found by Lemos. Moreover, the dRGT black string solution includes other classes of black string solution such as the monopole-black string ones since the graviton mass contributes to the global monopole term as well as the cosmological-constant term. To investigate the solution, we compute mass, temperature, and entropy of the dRGT black string. We found that the existence of the graviton mass drastically affects the thermodynamics of the black string. Furthermore, the Hawking-Page phase transition is found to be possible for the dRGT black string as well as the charged dRGT black string. The dRGT black string solution is thermodynamically stable for r > r c with negative thermodynamical potential and positive heat capacity while it is unstable for r < r c where the potential is positive.