Extreme Kerr black hole microstates with horizon fluff

TL;DR

This paper introduces a new family of solutions to Einstein's equations representing extremal Kerr black hole microstates, with a rich symmetry structure that allows for microstate counting matching the black hole's entropy and corrections.

Contribution

It constructs a phase space of microstates with a specific symmetry algebra, providing a novel approach to understanding Kerr black hole microstates and entropy.

Findings

Constructed a family of microstate solutions with conserved charges.

Identified a $U(1)$ Kac-Moody and Virasoro symmetry algebra.

Reproduced the Bekenstein-Hawking entropy and logarithmic corrections.

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.