Abstract
The gravitational description of black hole microstructure via the fuzzball proposal suggests a vast space of solutions called fuzzballs. This idea together with the 4d and 5d microscopic counting formulas necessitates that each supersymmetric 4d fuzzball admits an infinite number of hair. The hair removed fuzzballs are the true horizon degrees of freedom. We discuss how to construct/identify, count, and remove fuzzball hair.
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