This paper studies the thermodynamical stability of regular BHs in AdS5 background. We investigate off-shell free energy of the system as a function of temperature for different values of a "coupling constant" L=4 theta/l^2, where the cosmological constant is Lambda = -3/l^2 and \sqrt{ theta} is a "minimal length". The parameter L admits a critical value, L_{ inf}=0.2, corresponding to the appearance of an inflexion point in the Hawking temperature. In the weak-coupling regime L < L_{ inf}, there are first order phase transitions at different temperatures. Unlike the Hawking-Page case, at temperature 0\le T \le T_{ min} the ground state is populated by "cold" near-extremal BHs instead of a pure radiation. On the other hand, for L \g L_{ inf} only large, thermodynamically stable, BHs exist.
Categories: hep-th gr-qc hep-ph quant-ph