Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics

TL;DR

This paper derives the characteristic $T^{3/2}$ scaling of the low-temperature partition function for near-extremal black holes using quasinormal mode analysis, extending previous near-horizon methods to full black hole backgrounds.

Contribution

It provides a full-background derivation of the $T^{3/2}$ scaling for near-extremal BTZ black holes using the DHS formula and spectral measures, offering a new proof and potential extension to Kerr black holes.

Findings

Derived the spectral measure for fields in Euclidean BTZ.

Provided a new proof of the DHS formula.

Suggested a path to prove the $T^{3/2}$ scaling for Kerr black holes.

Abstract

Recent work on the quantum mechanics of near-extremal non-supersymmetric black holes has identified a characteristic $T^{3/2}$ scaling of the low temperature black hole partition function. This result has only been derived using the path integral in the near-horizon region and relies on many assumptions. We discuss how to derive the $T^{3/2}$ scaling for the near-extremal rotating BTZ black hole from a calculation in the full black hole background using the Denef-Hartnoll-Sachdev (DHS) formula, which expresses the 1-loop determinant of a thermal geometry in terms of a product over the quasinormal mode spectrum. We also derive the spectral measure for fields of any spin in Euclidean BTZ and use it to provide a new proof of the DHS formula and a new, direct derivation of the BTZ heat kernel. The computations suggest a path to proving the $T^{3/2}$ scaling for the asymptotically flat 4d Kerr black hole.