Black Hole Microstates and Entropy

The black hole entropy problem, often framed through the semi-classical relation between horizon area and entropy, challenges the consistency of quantum gravity and thermodynamic principles. Within the framework of string theory, Fuzzball solutions offer a nontrivial resolution by positing that black holes are ensembles of horizonless microstates, whose degeneracy matches the leading-order entropy scaling predicted by S ~ A. This paper conducts a comparative analysis of Fuzzball microstate geometries against other competing proposals, such as holographic dualities, where S_CFT asymptotically approaches black hole entropy and approaches derived from loop quantum gravity, which quantize spacetime at the Planck scale. Recent advancements in the moduli space of supersymmetric and near-extremal Fuzzball solutions have pushed forward our understanding of microstate counting, though extending these solutions to nonextremal configurations remains a formidable challenge. Moreover, the emergence of Hawking radiation as a coherent quantum process, while preserving unitarity, raises new questions about the completeness of the Fuzzball paradigm in resolving the information paradox. In this work, we explore the complex interplay between gravitational entropy, quantum information, and the non-local structure of spacetime, ultimately confronting the limitations and future directions of Fuzzball theory in addressing the full range of gravitational entropy phenomena.