http://arxiv.org/abs/1708.06378
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. This family of solutions form the “Extremal Kerr Phase Space”. We show the symplectic structure of this phase space remains invariant under a $U(1)$ Kac-Moody algebra which is generated by currents $\mathbb{J}_n$ and Virasoro generators $\mathbb{L}_n$ with central charge six times angular momentum of the black hole. This symplectic symmetry algebra is well-defined everywhere on the spacetime, near the horizon or in the asymptotic flat region. Out of 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 correctly reproduce the extreme Kerr black hole entropy.
K. Hajian, M. Sheikh-Jabbari and H. Yavartanoo
Wed, 23 Aug 17
21/45
Comments: 6 pages
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