Van der Waals black hole

TL;DR

This paper introduces a black hole solution in extended phase space whose thermodynamics mimic the Van der Waals fluid, but the solution violates energy conditions outside the horizon.

Contribution

It presents a novel asymptotically AdS black hole model with Van der Waals-like thermodynamics and analyzes its physical viability through energy condition violations.

Findings

Thermodynamics matches Van der Waals fluid exactly

The solution violates energy conditions outside the horizon

Provides insights into black hole thermodynamics in extended phase space

Abstract

In the context of extended phase space, where the negative cosmological constant is treated as a thermodynamic pressure in the first law of black hole thermodynamics, we find an asymptotically AdS metric whose thermodynamics matches exactly that of the Van der Waals fluid. However, we show that as a solution of Einstein's equations, the corresponding stress energy tensor does not obey any of the energy conditions everywhere outside of the horizon.