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 = 4θ/l2, where the cosmological constant is Λ = −3/l2
and
√
θ is “minimal length.” The parameter L admits a critical value, Linf = 0.2,
corresponding to the appearance of an inflexion point in the Hawking temperature. In
the weak-coupling regime L < Linf , there are first-order phase transitions at different
temperatures. Unlike the Hawking–Page case, at temperature 0 ≤ T ≤ Tmin the ground
state is populated by “cold” near-extremal BHs instead of a pure radiation. On the other
hand, for L > Linf , only large, thermodynamically stable BHs exist.
