A d-dimensional Reissner-Nordström black hole in a finite cavity has three equilibrium states below a critical charge and one above, and the two stable states undergo a first-order transition that becomes second-order at the critical charge.
Thermodynamics of Reissner-Nordstrom-anti-de Sitter black holes in the grand canonical ensemble
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abstract
The thermodynamical properties of the Reissner-Nordstr\"om-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 us 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. Instantons with negative heat capacity are also found.
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Canonical ensemble of a $d$-dimensional Reissner-Nordstr\"om black hole in a cavity
A d-dimensional Reissner-Nordström black hole in a finite cavity has three equilibrium states below a critical charge and one above, and the two stable states undergo a first-order transition that becomes second-order at the critical charge.