| Description |
1. We argue that for black holes which preserve at least four supersymmetries, the Wald entropy always equals the logarithm of a supersymmetric index. We verify this in several examples by computing the Wald entropy precisely and comparing with the exact microscopic counting. In all examples, when the microscopic degeneracy and index do not agree, it is the index that agrees with the macroscopic answer.
2. The general prescription for computing this index in the microscopic theory is not known. In simple situations in string theory, modular symmetry provides strong constrains on the black hole index. In situations with moduli dependence and wall-crossing, this modular property is destroyed. We show that in N = 4 theories, the black hole index is a {\it mock} modular form.
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