Black hole solution of Gauss-Bonnet massive gravity coupled to Maxwell and Yang-Mills fields in five dimensions

We construct a new static black hole solution of Gauss-Bonnet massive gravity coupled to Maxwell and Yang-Mills fields in five dimensions. We calculate the thermodynamical quantities of the black hole and check the first law of black hole thermodynamics. Thermal stability of the black hole is explored in the context of both canonical and grand canonical ensembles. By identifying the cosmological constant as the pressure of the gravitational system, we study the phase transitions of the black hole