Logarithmic Corrections to Kerr Thermodynamics

TL;DR

This paper extends the analysis of quantum corrections to black hole thermodynamics from charged black holes to near-extreme Kerr black holes, revealing logarithmic entropy corrections and a lifting of ground state degeneracy.

Contribution

It adapts the zero mode analysis and infrared regularization techniques to Kerr black holes, demonstrating similar logarithmic corrections and quantum effects as in charged black holes.

Findings

Quantum corrections induce a 3/2 log T_Hawking term in Kerr entropy.

Infrared divergence in the path integral is regulated by finite temperature effects.

Ground state degeneracy of extremal Kerr black holes is lifted by quantum effects.

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.