Enthalpy, geometric volume and logarithmic correction to entropy for van der Waals black hole

Abstract

If the negative cosmological constant is treated as a dynamical pressure and if the volume is its thermodynamically conjugate variable then the gravitational mass can be expressed as the total gravitational enthalpy rather than the energy. Under these circumtances, a new phenomenon emerges in the context of extended phase space thermodynamics. We examine here these features for the recently discovered van der Waals (VDW) black hole (BH) (Rajagopal A. et al., Phys. Lett. B, 737 (2014) 277) which is analogous to the VDW fluid. We show that the thermodynamic volume is greater than the naive geometric volume. We also show that the Smarr-Gibbs-Duhem relation is satisfied for this BH. Furthermore, by computing the thermal specific heat we find the local thermodynamic stability criterion for this BH. It has been observed that the BH does not possess any kind of second-order phase transition. This is an interesting feature of VDW BH by its own right. Moreover, we also derive the Cosmic-Censorship-Inequality for this class of BH. In addition finally, we compute the logarithmic correction to the entropy of this BH due to the quantum fluctuations around the thermal equilibrium.