A Universality Theorem for the Quantum Thermodynamics of Near-Extremal Black Holes

TL;DR

This paper proves a universal one-loop contribution to the thermodynamic entropy of near-extremal black holes across various spacetime geometries and symmetries, highlighting the role of tensor modes and Schwarzian modes.

Contribution

It establishes a universal theorem for the one-loop tensor mode contribution to black hole entropy, applicable to multiple black hole types and geometries.

Findings

Tensor mode contribution equals (3/2) log(T_Hawking/T_q)

Schwarzian modes appear universally in near-extremal geometries

The theorem applies to various symmetries and matter sectors

Abstract

We prove that the one-loop contribution from tensor modes to the thermodynamic entropy of near-extremal black holes is universal. Our proof applies to asymptotically flat, Anti-de-Sitter and de-Sitter black holes; it also covers spherical, axial and planar symmetries. We consider black hole configurations with and without matter sectors and explicitly discuss Abelian gauge fields and neutral scalar fields with arbitrary potential. We demonstrate that under certain conditions, the thermodynamics of near-extremal black holes contains a one-loop contribution from the tensor modes that equals $\frac{3}{2}\log (T_{\rm Hawking}/T_q)$. The proof of this theorem also shows explicitly how the Schwarzian modes appear universally in near-extremal geometries in dimensions four, five and six. We apply this theorem to Kerr-de-Sitter black holes as an explicit example.