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|Paper IPM / P / 14905||
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 \mathbbJn and Virasoro generators \mathbbLn 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 \bJn 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.
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