Extremal Kerr Entropy and the Attractor Mechanism

One of string theory's greatest successes has been its ability to provide a microscopic description for a large class of black holes, such that the thermodynamic entropy of those black holes can be reproduced at weak coupling by counting microstates. However, almost all such black holes exhibit supersymmetry, which does not manifest in our observable universe. On the other hand, non-supersymmetric black holes are usually too un-constrained and complicated to obtain a microscopic description. In between the two ends of the unphysical-complex spectrum lie extremal black holes, which are black holes that saturate the cosmic-censorship-required lower bound on their mass arising from their angular momentum or charge. Such black holes are not supersymmetric, but are constrained enough that a microscopic description in string theory is possible. The extremality condition also leads to attractor behavior, in which the asymptotic moduli of the theory are drawn to fixed values at the event horizon, determined only by the quantized charges of the black hole.

In this thesis, we review the string-theoretic description of the extremal Kerr black hole, and how that description can be used to compute the solution's statistical entropy at weak coupling. We then extend that work by applying the attractor mechanism to explain why the entropy at weak coupling matches the thermodynamic entropy at strong coupling.