One-Loop Corrections to Near-Extremal Kerr Thermodynamics from Semiclassical Virasoro Blocks

We propose a method to perform an exact calculation of one-loop quantum corrections to black hole entropy in terms of Virasoro semiclassical blocks. We analyze in detail a four-dimensional Kerr black hole and show that in the near-extremal limit a branch of long-lived modes arises. We prove that the contribution of these modes accounts for a (s-1/2)logT_{Hawking} correction to the entropy for massless particles of spin s=1, 2. We show that in the full calculation performed in the exact Kerr background the leading contribution actually is sourced by the near-horizon region only, and as such has a universal validity for any asymptotic behavior at infinity.