Thermodynamics of Reissner-Nordstrom-anti-de Sitter black holes in the grand canonical ensemble - art. no. 124007.

The thermodynamical properties of the Reissner-Nordstrom-anti-de Sitter bla ck hole in the grand canonical ensemble are investigated using York's forma lism. The black hole is enclosed in a cavity with a finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow one to compute the relevant thermodynamical quantities, e.g., therma l energy, entropy, and charge. The stability conditions imply that there ar e thermodynamically stable black hole solutions, under certain conditions. By taking the boundary to infinity, and leaving the event horizon and charg e of the black hole fixed, one rederives the Hawking-Page action and Hawkin g-Page specific heat. Instantons with negative heat capacity are also found . [S0556-2821(99)05108-5].