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Black Hole Phase Transitions and the Chemical Potential · Around

2015

Black Hole Phase Transitions and the Chemical Potential

Maity, Reevu, Roy, Pratim, Sarkar, Tapobrata

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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.

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