Dilaton Black Holes Near the Horizon

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Generic U(1)² 4-d black holes with unbroken N=1 supersymmetry are shown to tend to a Robinson-Bertotti type geometry with a linear dilaton and doubling of unbroken supersymmetries near the horizon. Purely magnetic dilatonic black holes, which have unbroken N=2 supersymmetry, behave near the horizon as a 2-d linear dilaton vacuum ⊗ S². This geometry is invariant under 8 supersymmetries, i.e. half of the original N=4 supersymmetries are unbroken. The supersymmetric positivity bound, which requires the mass of the 4-d dilaton black holes to be greater than or equal to the central charge, corresponds to positivity of mass for a class of stringy 2-d black holes.