Thermodynamics of Deformed AdS-Schwarzschild Black Hole

By implementing the gravitational decoupling method, we find the deformed AdS-Schwarzschild black hole solution when there is also an additional gravitational source, which obeys the weak energy condition. We also deliberately choose its energy density to be a certain monotonic function consistent with the constraints. In the method, there is a positive parameter that can adjust the strength of the effects of the geometric deformations on the background geometry, which we refer to as a deformation parameter. The condition of having an event horizon limits the value of the deformation parameter to an upper bound. After deriving various thermodynamic quantities as a function of the event horizon radius, we mostly focus on the effects of the deformation parameter on the horizon structure, the thermodynamics of the solution and the temperature of the Hawking- Page phase transition. The results show that with the increase of the deformation parameter: the minimum horizon radius required for a black hole to have local thermodynamic equilibrium and the minimum temperature below which there is no black hole decrease, and the horizon radius of the phase transition and the temperature of the first-order Hawking-Page phase transition increase. Furthermore, when the deformation parameter vanishes, the obtained thermodynamic behavior of the black hole is consistent with that stated in the literature.