In this paper, we studied the thermodynamic behavior of generalized warp factor for the corresponding AdS metric background. To discuss the stability of the theory we studied thermodynamical properties of generalized metric background. Here also to obtain the quantity of sound for the measure of stability of the system, we need to calculate the energy density and pressure. Such parameters of sound for the properties of stability constrain some conditions on the corresponding theory as θ. We used the corresponding conditions and rewrite the action of theory. The new action give us opportunity to study the AdS black hole and thermally charged AdS black hole.
