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In this note, we model the Bekenstein-Hawking entropy of a four dimensionalextremal black hole in terms of classifying particles moving in its nearhorizon AdS_2 geometry. We use the framework of SLE curves in AdS_2 to classifythese particle trajectories in terms of their boundary conditions. These turnout to be related to singular vectors in two-dimensional conformal quantumgravity theory in AdS_2 and the dynamics of these particles are governed by theHamiltonians of the integrable Calogero-like models, for these boundaryconditions. We use this classification to count the leading orderBekenstein-Hawking entropy of the black hole and arrive at a first principlemicroscopic computation of black hole degeneracy.

An SLE approach to four dimensional black hole microstate entropy