On Universal Constants of AdS Black Holes from Hawking-Page Phase Transition

We investigate the thermodynamic properties of the Hawking-Page phase transition of AdS black holes. We present evidence for the existence of two universal critical constants associated with the Hawking-Page (HP) and minimum black hole thermodynamical transition points. These constants are defined by C_S =\frac{S_{HP}-S_{min}}{S_{min}} and C_T =\frac{T_{HP}-T_{min}}{T_{min}} where S_{min}(S_{HP}) and T_{min}(T_{HP}) are the minimal (HP phase transition) entropy and temperature, respectively, below which no black hole can exist. For a large class of four dimensional non-rotating black holes, we find C_S =2 and C_T = \frac{2-\sqrt{3}}{\sqrt{3}}. For the rotating case, however, such universal ratios are slightly affected without losing the expected values. Taking small values of the involved rotating parameter, we recover the same constants. Higher dimensional models, with other universal constants, are also discussed in some details.