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The fuzzball proposal for black holes: an elementary review

Samir D. Mathur

TL;DR

The fuzzball proposal reframes black holes in string theory as ensembles of horizonless microstate geometries whose boundary area reproduces the Bekenstein entropy $S_{Bek}=A/4G$. By counting microstates for two- and three-charge BPS bound states (NS1-NS5-P and D1-D5-P) and constructing explicit horizonless geometries via profile functions $\vec{F}(v)$, the work shows $S_{micro}$ matches $S_{Bek}$ and that horizons are replaced by smooth caps. Dualities relate different brane descriptions and reveal a universal cap structure across frames, strengthening the case that information can be preserved in the radiation emitted by fuzzballs. Collectively, these results suggest a deep link between the phase-space counting of microstates and the geometric realization of black hole interiors, with potential extensions to non-BPS cases and implications for the resolution of the information paradox.

Abstract

We give an elementary review of black holes in string theory. We discuss BPS holes, the microscopic computation of entropy and the `fuzzball' picture of the black hole interior suggested by microstates of the 2-charge system.

The fuzzball proposal for black holes: an elementary review

TL;DR

The fuzzball proposal reframes black holes in string theory as ensembles of horizonless microstate geometries whose boundary area reproduces the Bekenstein entropy . By counting microstates for two- and three-charge BPS bound states (NS1-NS5-P and D1-D5-P) and constructing explicit horizonless geometries via profile functions , the work shows matches and that horizons are replaced by smooth caps. Dualities relate different brane descriptions and reveal a universal cap structure across frames, strengthening the case that information can be preserved in the radiation emitted by fuzzballs. Collectively, these results suggest a deep link between the phase-space counting of microstates and the geometric realization of black hole interiors, with potential extensions to non-BPS cases and implications for the resolution of the information paradox.

Abstract

We give an elementary review of black holes in string theory. We discuss BPS holes, the microscopic computation of entropy and the `fuzzball' picture of the black hole interior suggested by microstates of the 2-charge system.

Paper Structure

This paper contains 21 sections, 172 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Making black holes in string theory
  3. BPS states
  4. The 1-charge solution
  5. Two charges
  6. Three charges
  7. Dualities
  8. The microscopic count of states
  9. Bound states and unbound states
  10. Entropy of the NS1-P bound state
  11. Entropy for the three charge state
  12. Constructing the microstates
  13. Obtaining the D1-D5 geometries
  14. A special example
  15. Regularity of the general solution
  16. ...and 6 more sections

Figures (2)

  • Figure 1: (a) The conventional picture of a black hole (b) the proposed picture -- state information is distributed throughout the 'fuzzball'.
  • Figure 2: (a) The naive geometry of extremal D1-D5 (b) the actual geometries; the area of the surface denoted by the dashed line reproduces the microscopic entropy.