Holography, thermodynamics, and fluctuations of charged AdS black holes

The physical properties of Reissner-Nordström black holes in $\mathrm{}(n+1\mathrm{})\mathrm{}$-dimensional anti–de Sitter spacetime are related, by a holographic map, to the physics of a class of $n$-dimensional field theories coupled to a background global current. Motivated by that fact, and the recent observations of the striking similarity between the thermodynamic phase structure of these black holes (in the canonical ensemble) and that of the van der Waals–Maxwell liquid-gas system, we explore the physics in more detail. We study fluctuations and stability within the equilibrium thermodynamics, examining the specific heats and electrical permittivity of the holes, and consider the analogue of the Clayperon equation at the phase boundaries. Consequently, we refine the phase diagrams in the canonical and grand canonical ensembles. We study the interesting physics in the neighborhood of the critical point in the canonical ensemble. There is a second order phase transition found there, and that region is characterized by a Landau-Ginzburg model with $A_3$ potential. The holographically dual field theories provide the description of the microscopic degrees of freedom which underlie all of the thermodynamics, as can be seen by examining the form of the microscopic fluctuations.