Volume dependent extension of Kerr-Newman black hole thermodynamics

TL;DR

This paper extends Kerr-Newman black hole thermodynamics by incorporating a pressure term from Hawking radiation, modifying entropy, defining a thermodynamic volume, and deriving a stable equation of state.

Contribution

It introduces a volume-dependent extension to black hole thermodynamics, accounting for radiation pressure and redefining entropy and volume relations.

Findings

Entropy is modified by a factor of 8/3 due to radiation pressure.

Thermodynamic volume scales as V ~ M^5, consistent with other models.

The effective equation of state is stable with S(E,V) ~ E^{3/4}V^{1/4}.

Abstract

We show that the Hawking--Bekenstein entropy formula is modified by a factor of $8/3$ if one also considers a work term in the 1st law of thermodynamics by a pressure stemming from the Hawking radiation. We give an intuitive definition for the corresponding thermodynamical volume by the implicit definition $\epsilon=Mc^2/V$, which is the average energy density of the Hawking radiation. This volume scales as $V \sim M^5$, agreeing with other suggestions. As a result the corresponding Smarr relation describes an extensive entropy and a stable effective equation of state $S(E,V)\sim E^{3/4}V^{1/4}$. These results pertain for charged and rotating Kerr-Newman black holes.