Thermodynamics of Reissner–Nordström–anti-de Sitter black holes in the grand canonical ensemble

Abstract

The thermodynamical properties of the Reissner-Nordström-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 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.

P − V criticality of charged AdS black holes

“…Inspecting the critical values (3.17) we find an interesting relation 19) which is exactly the same as for the Van der Waals fluid and is a universal number predicted for any RN-AdS black hole with arbitrary charge. Moreover the critical values (3.17) can be written in the form (2.4), with…”

Holography of charged black holes withRF2corrections

“…Thermodynamics of charged black holes was extensively investigated in e.g. [15,16,17,18]. First the temperature is given by The other thermodynamic quantities can be evaluated in a standard way.…”

Classical instability of Kerr-AdS black holes and the issue of final state

“…It is then natural to argue that the Hawking-Page phase transition in the gravity side of the duality corresponds to a confinement/deconfinement transition in the CFT side [2,5]. A number of other asymptotically AdS black holes have been studied, and their thermodynamical properties thoroughly investigated: charged [6,7,8,9,10,11,12,13], rotating [12,13,14,15], and non-spherical [16,17,18] black holes, and their interpretation in the AdS/CFT duality context.…”