Firstly, we explore the microstates of the small black hole in the 1/2-BPS sector of AdS₅xS₅, referred to as the "superstar", using the powerful holographic description provided by LLM. The system's distinctiveness lies in its inherent statistical application to the black holes. Notably, the geometry of superstar only emerges upon averaging over an ensemble of geometries. The individual microstate geometries are differentiated by the highly non-trivial topology of a quantum foam at their core, and entropy can be comprehended as a partition of N units of flux among 5-cycles, as necessitated by flux quantization.

Interestingly, while the system offers confirmation on the most disputed aspect of Mathur and Lunin's recent "fuzzball" proposal, observers should anticipate a discrepancy in the interpretation of its details.

Introduction

Holography promises a resolution to many unresolved issues in general relativity due to its abilities to define a full quantum-mechanical explanation of gravity in a dual gauge theory. However, with the construction of both sides of the duality turning out to be complex, many queries have gradually revealed their mysteries. A recent contribution by Lin, Lunin and Maldacena managed an explicit breakthrough in understanding a non-trivial sector of the AdS/CFT duality, revealing fascinating new structural properties.

This breakthrough can be applied to tackle critical issues in quantum gravitation, such as chronology protection and studying topology-changing transitions to demonstrate a widely accepted smooth merger of fermi droplets in the dual theory. As a result, any mystery surrounding quantum gravity could be dissected using LLM's unraveling of quantum gravity.

The Superstar

In the 1/2-BPS sector of excitations on AdS₅xS₅, a non-supersymmetric family of asymptotically AdS₅xS₅ black holes exist, as discovered by Myers and Tafjord. These black holes preserve half the supersymmetry, presenting a legitimate preview of black hole physics. After evaluating α' corrections, we suppose a proper lift from a superstar to an actual black hole.

Review of LLM

Thanks to LLM's solution to AdS/CFT correspondence, we can delve deep into black hole physics in a fully quantum-mechanical setting, therby comprehending free fermions in a harmonic oscillator potential.

This study offers a quantum mechanical exploration into black hole physics. Additionally, it emphasises the inherently statistical nature of black holes and indicates the possibility of a discrepancy in interpreting the details. Moreover, this knowledge brings us a step closer to understanding the mysteries of quantum gravity.