Thermodynamical properties of black holes in R²-dRGT massive gravity

Massive gravity is an intriguing and significant modification of general relativity, as it proposes a nonzero mass for the graviton. In this talk, we present a specific model of massive gravity known as the de Rham, Gabadadze, and Tolley (dRGT) massive gravity model, extended to include a higher order curvature gravity term. We obtain a spherically symmetric solution for the field equations. We examine the thermodynamics of the black hole solution and find the thermodynamic quantities, such as temperature, heat capacity, and Helmholtz free energy of the black hole. Our results show that the massive graviton and the higher order gravity term affect the black hole's thermodynamical properties. Also, using the observational constraints on the coefficient of the higher order term, we determine an upper limit for the graviton mass.