Black Hole Statistics from Holography

TL;DR

This paper investigates the microstates of a small BPS black hole in AdS5×S5 using holography, revealing the statistical nature of black hole geometry and microstate topology, and discussing implications for the fuzzball proposal.

Contribution

It provides a detailed holographic analysis of black hole microstates, highlighting their topological diversity and entropy partitioning, and offers insights into the fuzzball conjecture.

Findings

Microstates exhibit complex topology with quantum foam structure.

Black hole entropy corresponds to flux partitioning among cycles.

Supports aspects of the fuzzball proposal but indicates some discrepancies.

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.