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Phase transition and thermodynamic stability in extended phase space and charged Hořava-Lifshitz black holes. (English) Zbl 1381.83077

Summary: For charged black holes in Hořava-Lifshitz gravity, a second order phase transition takes place in extended phase space where the cosmological constant is taken as thermodynamic pressure. We relate the second order nature of phase transition to the fact that the phase transition occurs at a sharp temperature and not over a temperature interval. Once we know the continuity of the first derivatives of the Gibbs free energy, we show that all the Ehrenfest equations are readily satisfied. We study the effect of the perturbation of the cosmological constant as well as the perturbation of the electric charge on thermodynamic stability of Hořava-Lifshitz black hole. We also use thermodynamic geometry to study phase transition in extended phase space. We investigate the behavior of scalar curvature of Weinhold, Ruppeiner, and Quevedo metric in extended phase space of charged Hořava-Lifshitz black holes. It is checked if these curvatures could reproduce the result of specific heat for the phase transition.

MSC:

83C57 Black holes
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
80A10 Classical and relativistic thermodynamics
83C22 Einstein-Maxwell equations
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