Black Hole Phase Transitions and the Chemical Potential
Abstract
In the context of extended phase space thermodynamics and the AdSCFT 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 HawkingPage transition for AdSSchwarzschild and RNAdS black holes in five dimensions, signalling the onset of quantum effects at the transition point. Such behaviour is absent for nonrotating black holes in four dimensions. For KerrAdS 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 HawkingPage transition temperature, for a range of angular frequencies. We also analyse AdS black holes in five dimensional GaussBonnet gravity, and find similar features for $\mu$ as in the KerrAdS case.
 Publication:

arXiv eprints
 Pub Date:
 December 2015
 arXiv:
 arXiv:1512.05541
 Bibcode:
 2015arXiv151205541M
 Keywords:

 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 1 + 14 Pages, LaTeX, 6 .eps figures