Extended phase space thermodynamics for charged and rotating black holes and Born-Infeld vacuum polarization

TL;DR

This paper explores the thermodynamic phase transitions of charged and rotating AdS black holes in various dimensions, incorporating non-linear electrodynamics via Born-Infeld theory, and introduces a new thermodynamic quantity called Born-Infeld vacuum polarization.

Contribution

It extends black hole thermodynamics to include Born-Infeld vacuum polarization and analyzes critical phenomena across different dimensions and black hole types.

Findings

Reissner-Nordstrom black holes exhibit Van der Waals-like phase transitions in dimensions > 3.

Neutral slowly rotating black holes in 4D show similar critical behavior.

Born-Infeld vacuum polarization is essential for thermodynamic consistency.

Abstract

We investigate the critical behaviour of charged and rotating AdS black holes in d spacetime dimensions, including effects from non-linear electrodynamics via the Born-Infeld action, in an extended phase space in which the cosmological constant is interpreted as thermodynamic pressure. For Reissner-Nordstrom black holes we find that the analogy with the Van der Walls liquid-gas system holds in any dimension greater than three, and that the critical exponents coincide with those of the Van der Waals system. We find that neutral slowly rotating black holes in four space-time dimensions also have the same qualitative behaviour. However charged and rotating black holes in three spacetime dimensions do not exhibit critical phenomena. For Born-Infeld black holes we define a new thermodynamic quantity B conjugate to the Born-Infeld parameter b that we call Born-Infeld vacuum polarization. We demonstrate that this quantity is required for consistency of both the first law of thermodynamics and the corresponding Smarr relation.