Black holes in R2-dRGT massive gravity

Abstract

Massive gravity offers an interesting modification of general relativity by considering a nonzero mass for the graviton. We present a de Rham, Gabadadze and Tolley (dRGT) massive gravity model in the presence of higher order curvature gravity. We obtain a spherical solution for the field equations in this theory. The spherical solution possesses an electric charge and a cosmological constant, and it reduces to the Schwarzschild solution in the limit of a negligible graviton mass and the absence of the higher order term. We study the thermodynamics of this black hole and find that the mass of the graviton and the higher order term of gravity have a significant effect on the thermodynamic properties of the black hole. We also show the entropy of a black hole is independent of the mass of the graviton. Using the observational constraints on the coefficient of the higher order term, we determine an upper limit for the graviton mass. We compute the other thermodynamic quantities, such as heat capacity and Helmholtz free energy. Assuming that the spherical solutions are the modified Schwarzschild, we consider the relativistic thin accretion disk and study the effects of higher order term on thermal properties of the disk at the infrared limit in an asymptotic safety scenario.