Van Der Waals Black Holes in $d$ dimensions

TL;DR

This paper extends Van Der Waals black hole solutions to arbitrary dimensions and topologies, interpreting the metric as a near horizon solution and comparing it to known black holes like Reissner-Nordström.

Contribution

It generalizes VDW black hole solutions to higher dimensions and different topologies, providing a new interpretation as near horizon metrics and analyzing their relation to known black holes.

Findings

VDW black hole metric is a near horizon solution.

Mapping of fluid equations of state to black hole solutions.

Reissner-Nordström and VDW black holes are qualitatively similar near the horizon.

Abstract

We generalize the recent solution proposed by Rajagopal et al. to arbitrary number of dimensions and horizon topologies. We comment on the regime of validity of these solution. Among our main results, we argue that the Van Der Waals (VDW) black hole (BH) metric is to be interpreted as a near horizon metric. This is supported by inspecting the energy conditions. We analyze the limiting cases of a perfect fluid, interacting points and non interacting balls gas equation of state and map them to known black holes. Finally, we provide a case study by comparing the Reissner-Nordstr\"om and VDW BH close to the horizon and show that they are qualitatively similar for some range of the horizon radius.