Logarithmic Corrections to Kerr Thermodynamics

Kapec, Daniel; Sheta, Ahmed; Strominger, Andrew; Toldo, Chiara

doi:10.1103/PhysRevLett.133.021601

Logarithmic Corrections to Kerr Thermodynamics

Journal Article · Tue Jul 09 00:00:00 EDT 2024 · Physical Review Letters

DOI:https://doi.org/10.1103/PhysRevLett.133.021601· OSTI ID:2396405

; ; Strominger, Andrew;

Recent work has shown that loop corrections from massless particles generate $\frac{3}{2} \log T_{Hawking}$ corrections to black hole entropy which dominate the thermodynamics of cold near-extreme charged black holes. Here we adapt this analysis to near-extreme Kerr black holes. Like ${AdS}_{2} \times S^{2}$ , the near-horizon extreme Kerr (NHEK) metric has a family of normalizable zero modes corresponding to reparametrizations of boundary time. The path integral over these zero modes leads to an infrared divergence in the one-loop approximation to the Euclidean NHEK partition function. We regulate this divergence by retaining the leading finite temperature correction in the NHEK scaling limit. This “not-NHEK” geometry lifts the eigenvalues of the zero modes, rendering the path integral infrared finite. The quantum-corrected near-extremal entropy exhibits $\frac{3}{2} \log T_{Hawking}$ behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.

Published by the American Physical Society 2024

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Research Organization:: Harvard Univ., Cambridge, MA (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: SC0007870

OSTI ID:: 2396405

Alternate ID(s):: OSTI ID: 2579721

Journal Information:: Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 2 Vol. 133; ISSN 0031-9007; ISSN PRLTAO

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

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