A class of black holes in dRGT massive gravity and their thermodynamical properties

Abstract

We present exact spherical black hole solutions 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 canonical ensembles (for charged case). It turns out that the dGRT black hole solutions includes the known solutions to the Einstein field equations, such as, the monopole-de Sitter-Schwarzschild ones with the coefficients for 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 dGRT black hole solutions and also perform thermodynamical stability. It turns out that the presence of the graviton mass completely changes the black hole thermodynamics, and it can provide the Hawking-Page phase transition which is also true for the obtained charged black holes. Interestingly, the entropy of a black hole is unaffected and still obeys area law. In particular, our results, in the limit $m_g \rightarrow 0$, reduced exactly to \emph{vis-$\grave{a}$-vis} the general relativity results.