Charged $AdS$ Black Holes in $4D$ Einstein--Gauss--Bonnet Massive Gravity

Abstract: We investigate Einstein--Gauss--Bonnet--Maxwell massive gravity in $4D$ AdS background and find an exact black hole solution. The horizon structure of the black holes studied. Treating the cosmological constant as pressure and Gauss-Bonnet coupling parameters, and massive gravity parameters as variables, we drive the first law of black hole thermodynamics. To study the global stability of the black holes we compute the Gibbs free energy. The local stability of the black hole is also studied through specific heat. We analyze the effects of graviton mass and Gauss-Bonnet coupling parameters on the phase transition of the black holes. Finally, the effects of graviton mass and massive gravity parameters on the Joule-Thomson expansion of the black hole are studied.