Criticality and Surface Tension in Rotating Horizon Thermodynamics

TL;DR

This paper explores a modified thermodynamics framework for rotating black holes, revealing a new horizon first law with surface tension and analyzing the critical behavior and equations of state in this context.

Contribution

It introduces a cohomogeneity two horizon first law including surface tension and studies the critical phenomena in rotating black hole thermodynamics.

Findings

Derived a horizon first law with surface tension for rotating black holes.

Obtained a universal equation of state and analyzed critical behavior.

Simplified to a cohomogeneity one law with pressure and volume for fixed angular momentum.

Abstract

We study a modified horizon thermodynamics and the associated criticality for rotating black hole spacetimes. Namely, we show that under a virtual displacement of the black hole horizon accompanied by an independent variation of the rotation parameter, the radial Einstein equation takes a form of a "cohomogeneity two" horizon first law, $dE=TdS+\Omega dJ-\sigma dA$, where $E$ and $J$ are the horizon energy (an analogue of the Misner-Sharp mass) and the horizon angular momentum, $\Omega$ is the horizon angular velocity, $A$ is the horizon area, and $\sigma$ is the surface tension induced by the matter fields. For fixed angular momentum, the above equation simplifies and the more familiar (cohomogeneity one) horizon first law $dE=TdS-PdV$ is obtained, where $P$ is the pressure of matter fields and $V$ is the horizon volume. A universal equation of state is obtained in each case and the corresponding critical behavior is studied.