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The quantum structure of black holes

Samir D. Mathur

TL;DR

<3-5 sentence high-level summary>The paper surveys how string theory accounts for black hole entropy and Hawking radiation through explicit microstates of brane bound states, especially NS1-NS5-P. It introduces and develops the fuzzball picture, where horizon-sized, horizonless microstate geometries replace the traditional black hole interior, and demonstrates entropy counting and radiation matching for 2-, 3-, and 4-charge holes via bound-state fractionation. Through detailed constructions of microstate geometries and analysis of bound-state sizes, the work argues that the black hole interior is replaced by a rich family of microstate geometries whose boundary areas reproduce the Bekenstein entropy and whose dynamics reproduce Hawking emission, offering a potential resolution to the information paradox in these regimes. The results imply that nonperturbative string effects can extend to macroscopic scales, with fractionation driving both large entropy and large bound-state sizes, though a complete nonextremal microscopic theory remains a frontier for future work.

Abstract

We give an elementary review of black holes in string theory. We discuss black hole entropy from string microstates and Hawking radiation from these states. We then review the structure of 2-charge microstates, and explore how `fractionation' can lead to quantum effects over macroscopic length scales of order the horizon radius.

The quantum structure of black holes

TL;DR

<3-5 sentence high-level summary>The paper surveys how string theory accounts for black hole entropy and Hawking radiation through explicit microstates of brane bound states, especially NS1-NS5-P. It introduces and develops the fuzzball picture, where horizon-sized, horizonless microstate geometries replace the traditional black hole interior, and demonstrates entropy counting and radiation matching for 2-, 3-, and 4-charge holes via bound-state fractionation. Through detailed constructions of microstate geometries and analysis of bound-state sizes, the work argues that the black hole interior is replaced by a rich family of microstate geometries whose boundary areas reproduce the Bekenstein entropy and whose dynamics reproduce Hawking emission, offering a potential resolution to the information paradox in these regimes. The results imply that nonperturbative string effects can extend to macroscopic scales, with fractionation driving both large entropy and large bound-state sizes, though a complete nonextremal microscopic theory remains a frontier for future work.

Abstract

We give an elementary review of black holes in string theory. We discuss black hole entropy from string microstates and Hawking radiation from these states. We then review the structure of 2-charge microstates, and explore how `fractionation' can lead to quantum effects over macroscopic length scales of order the horizon radius.

Paper Structure

This paper contains 39 sections, 287 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Making black holes in string theory
  3. Two charges
  4. Three charges
  5. Dualities
  6. The microscopic count of states
  7. Extremal NS1-P
  8. Extremal NS1-NS5-P
  9. Non-extremal holes
  10. The nonextremal gravity solution
  11. The extremal limit: 'Three large charges, no nonextremality'
  12. Two large charges $+$ nonextremality
  13. One large charge $+$ nonextremality
  14. No large charges
  15. The 4-charge hole
  16. ...and 24 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 NS1-NS5 (b) the actual geometries; the area of the surface denoted by the dashed line reproduces the microscopic entropy.