Extreme Kerr black hole microstates with horizon fluff

Abstract

We present a one-function family of solutions to 4D vacuum Einstein equations. While all diffeomorphic to the same extremal Kerr black hole, they are labeled by well-defined conserved charges and are hence distinct geometries. We show that this family of solutions forms a phase space the symplectic structure of which is invariant under a $U(1)$ Kac-Moody algebra generated by currents ${\mathbb{J}}_n$ and Virasoro generators ${\mathbb{L}}_n$ with central charge six times angular momentum of the black hole. This symmetry algebra is well-defined everywhere in the spacetime, near the horizon or in the asymptotic flat region. Out of the appropriate combination of ${\mathbb{J}}_n$ charges, we construct another Virasoro algebra at the same central charge. Requiring that these two Virasoro algebras should describe the same system leads us to a proposal for identifying extreme Kerr black hole microstates, dubbed as extreme Kerr fluff. Counting these microstates, we not only correctly reproduce the Bekenstein-Hawking entropy of extreme Kerr black hole, but also its expected logarithmic corrections.

8 pages, published version

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Cited by in corpus (5)

• Coupling Constants as Conserved Charges in Black Hole Thermodynamics
• Near horizon symmetries, emergence of Goldstone modes and thermality
• Microscopic states of Kerr black holes from boundary-bulk correspondence
• BMS Goldstone modes near the horizon of a Kerr black hole are thermal
• Single-rotating Five-dimensional Near-horizon Extremal Geometry in General Relativity