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 black hole in the grand canonical ensemble are investigated using York's formalism. 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., thermal energy, entropy, and charge. The stability conditions imply that there are thermodynamically stable black hole solutions, under certain conditions. By taking the boundary to infinity, and leaving the event horizon and charge of the black hole fixed, one rederives the Hawking-Page action and Hawking-Page specific heat. Instantons with negative heat capacity are also found. [S0556-2821(99)05108-5].