Logarithmic Corrections to Kerr Thermodynamics

Abstract

Recent work has shown that loop corrections from massless particles generate $\frac{3}{2}\log T_{\text{Hawking}}$ 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 $\frac{3}{2}\log T_{\text{Hawking}}$ behavior characteristic of the Schwarzian model and predicts a lifting of the ground state degeneracy for the extremal Kerr black hole.

arXiv comment14 pages

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• pp-Waves and the Hidden Symmetries of Black Hole Quasinormal Modes
• Les Houches lectures on two-dimensional gravity and holography
• Quasinormal Corrections to Near-Extremal Black Hole Thermodynamics
• Quantum-Corrected Hawking Radiation from Near-Extremal Kerr-Newman Black Holes
• Logarithmic Corrections to Thermodynamics of Accelerating Black Holes
• Extremal Black Holes from Homotopy Algebras
• One-loop effect in the charged 2D black hole near extremality