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Paper IPM / P / 14905  


Abstract:  
We present a onefunction family of solutions to 4D vacuum Einstein equations. While all diffeomorphic to the same extremal Kerr black hole, they are labeled by welldefined 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) KacMoody algebra which is generated by currents \mathbbJ_{n} and Virasoro generators \mathbbL_{n} with central charge six times angular momentum of the black hole. This symplectic symmetry algebra is welldefined everywhere on the spacetime, near the horizon or in the asymptotic flat region. Out of appropriate combination of \bJ_{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.
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