Explicit black hole thermodynamics in natural variables

Abstract

We consider the general thermal asymptotically flat Kerr-Newman black holes in 4d Einstein-Maxwell theory. Even though their thermodynamics has been understood for decades, the Gibbs free energy and on-shell action are only known implicitly as functions of the standard chemical potentials. Using the so-called left and right moving (or holomorphic and anti-holomorphic) variables related to the chemical potentials on both the outer and the inner horizons, we are able to present explicit and very simple expressions for all quantities. We discuss various limits in the parameter space, remarkably finding a smooth BPS limit allowing direct access to the extremal surface. In the BPS limit the anti-holomorphic part of the on-shell action vanishes identically, leading automatically to the holomorphic expression expected microscopically. This gives us confidence that the newly defined thermal partition function in terms of these variables is the natural candidate for a full microscopic description.

5 pages; v2 minor corrections

References in corpus (4)

• Universal Area Product Formulae for Rotating and Charged Black Holes in Four and Higher Dimensions
• Inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory
• The dark (BPS) side of thermodynamics in Minkowski${}_4$
• Explicit black hole thermodynamics in natural variables

Cited by in corpus (3)

• Explicit black hole thermodynamics in natural variables
• Black hole thermodynamics at 4 derivatives, natural variables and BPS limits
• Notes on sums over horizons