Black Hole Phase Transitions and the Chemical Potential

Abstract

In the context of extended phase space thermodynamics and the AdS-CFT correspondence, we consider the chemical potential ($\mu$) dual to the number of colours ($N$) of the boundary gauge theory, in the grand canonical ensemble. By appropriately defining $\mu$ via densities of thermodynamic quantities, we show that it changes sign precisely at the Hawking-Page transition for AdS-Schwarzschild and RN-AdS black holes in five dimensions, signalling the onset of quantum effects at the transition point. Such behaviour is absent for non-rotating black holes in four dimensions. For Kerr-AdS black holes in four and five dimensions, our analysis points to the fact that $\mu$ can change sign in the stable black hole region, i.e above the Hawking-Page transition temperature, for a range of angular frequencies. We also analyse AdS black holes in five dimensional Gauss-Bonnet gravity, and find similar features for $\mu$ as in the Kerr-AdS case.

1 + 14 Pages, LaTeX, 6 .eps figures

References in corpus (3)

• Black Hole Enthalpy and an Entropy Inequality for the Thermodynamic Volume
• Phase transition and Thermodynamical geometry of Reissner-Nordström-AdS Black Holes in Extended Phase Space
• Bose condensation and branes

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