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arXiv · 2409.14928

Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics

Daniel Kapec·Y. T. Albert Law·Chiara Toldo
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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.

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Daniel Kapec, Y. T. Albert Law, Chiara Toldo. 2024-09-23. Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics. https://doi.org/10.1007/jhep06(2025)069

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