The fuzzball proposal for black holes

TL;DR

The fuzzball proposal reframes black holes as ensembles of horizon-free microstate geometries, each corresponding to a distinct CFT state and collectively accounting for the Bekenstein–Hawking entropy. By leveraging AdS/CFT and holographic renormalization, KK holography, and explicit D1-D5 microstate constructions, the paper compiles substantial evidence that many black hole microstates are realized as smooth, horizonless geometries, with vevs of gauge-invariant operators encoding state information. It reviews two-, three-, and four-charge systems, detailing explicit fuzzball solutions, the state–geometry dictionary, and tests via one-point functions, flight times, and geometric quantization, while highlighting open questions about stringy fuzzballs, coarse-graining, and the emergence of horizons. The work underscores the crucial role of going beyond supergravity to fully capture the microstate structure and argues that holography provides a natural framework to address information loss and horizon physics, albeit with substantial technical challenges remaining. Collectively, these developments point toward a holographically grounded, microstate-resolved view of black holes, while signaling that a complete, stringy understanding of fuzzballs and their ensemble behavior is essential for a definitive resolution of BH puzzles.

Abstract

The fuzzball proposal states that associated with a black hole of entropy S there are exp S horizon-free non-singular solutions that asymptotically look like the black hole but generically differ from the black hole up to the horizon scale. These solutions, the fuzzballs, are considered to be the black hole microstates while the original black hole represents the average description of the system. The purpose of this report is to review current evidence for the fuzzball proposal, emphasizing the use of AdS/CFT methods in developing and testing the proposal. In particular, we discuss the status of the proposal for 2 and 3 charge black holes in the D1-D5 system, presenting new derivations and streamlining the discussion of their properties. Results to date support the fuzzball proposal but further progress is likely to require going beyond the supergravity approximation and sharpening the definition of a "stringy fuzzball". We outline how the fuzzball proposal could resolve longstanding issues in black hole physics, such as Hawking radiation and information loss. Our emphasis throughout is on connecting different developments and identifying open problems and directions for future research.