Extreme Kerr black hole microstates with horizon fluff

Understand

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.