Black Hole Statistics from Holography

Abstract

We study the microstates of the ``small'' black hole in the $\half$-BPS sector of AdS$_5\times S^5$, the superstar of Myers and Tafjord, using the powerful holographic description provided by LLM. The system demonstrates the inherently statistical nature of black holes, with the geometry of Myer and Tafjord emerging only after averaging over an ensemble of geometries. The individual microstate geometries differ in the highly non-trivial topology of a quantum foam at their core, and the entropy can be understood as a partition of $N$ units of flux among 5-cycles, as required by flux quantization. While the system offers confirmation of the most controversial aspect of Mathur and Lunin's recent ``fuzzball'' proposal, we see signs of a discrepancy in interpreting its details.