Phase transition and thermodynamic stability in extended phase space and charged Hořava–Lifshitz black holes

Abstract

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.

Phase transitions in four-dimensional AdS black holes with a nonlinear electrodynamics source

“…Therefore, there are three different phases that we call an SBH, meta-stable black hole (MBH) and LBH; some results have been reported for charged AdS black holes with Maxwell and PMIs in [66][67][68]. Now, to determine the second-order phase transition and its consequences we study the critical behaviour by performing a comparison of the equations of state with the van der Waals equation.…”

Phase transitions in four-dimensional AdS black holes with a nonlinear electrodynamics source

“…Then, we can recognize three different phases, two stables phases where C Q > 0 for small and large horizon radius, and one unstable phase C Q < 0 for intermediate radius. Therefore, there are three different phases that we call small black hole (SBH), meta-stable black hole (MBH) and large black hole (LBH), some results have been reported for charged AdS black holes with Maxwell and power Maxwell invariants in [51][52][53]. Now, in order to figure out the second order phase transition and its consequences we study the critical behaviour performing the comparison of the equations of state with the Van der Waals equation.…”

Dynamic Analytical Solution of a Charged Dilaton Black Hole

“…Whether the parameters involved in different black holes affect the system is also a significant problem. In the extended phase space, the influence of the perturbation of the cosmological constant, the charge, and the massive gravity was analyzed for the black holes with the background of charged Hořava-Lifshitz and massive gravity [46,47]. For the black hole in de Rham, Gabadadze, and Tolley's massive gravity in new extended phase space, the influence of distinct values of the spacetime parameters on the thermodynamic stability was also presented [48].…”