Thermodynamics of the near-extremal Kerr spacetime

TL;DR

This paper analyzes the thermodynamics of near-extremal Kerr black holes, showing they behave as quantum systems with small degeneracy at low temperatures, contrasting classical predictions of large entropy.

Contribution

It provides a detailed gravitational path integral analysis revealing the quantum nature of near-extremal Kerr black holes and computes the low-temperature partition function behavior.

Findings

Low temperature partition function scales as T^{3/2} with entropy corrections.

Near-extremal Kerr black holes exhibit a vanishing degeneracy, unlike classical predictions.

Rotational zero modes influence the thermodynamic coefficients and raise theoretical puzzles.

Abstract

We examine the thermodynamics of a near-extremal Kerr black hole, and demonstrate that the geometry behaves as an ordinary quantum system with a vanishingly small degeneracy at low temperatures. This is in contrast with the classical analysis, which instead predicts a macroscopic entropy for the extremal Kerr black hole. Our results follow from a careful analysis of the gravitational path integral. Specifically, the low temperature canonical partition function behaves as $Z \sim \, T^\frac{3}{2}\, e^{S_0+ c \log S_0}$, with $S_0$ the classical degeneracy and $c$ a numerical coefficient we compute. This is in line with the general expectations for non-supersymmetric near-extremal black hole thermodynamics, as has been clarified in the recent past, although cases without spherical symmetry have not yet been fully analyzed until now. We also point out some curious features relating to the rotational zero modes of the near-extremal Kerr black hole background that affects the coefficient $c$. This raises a puzzle when considering similar black holes in string theory. Our results generalize to other rotating black holes, as we briefly exemplify.