Where are the states of a black hole?

TL;DR

Mathur argues that black hole microstates are realized as horizonless 'fuzzball' geometries in string theory, with entropy arising from coarse-graining over interior hair rather than a single horizon per state. The 2-charged D1-D5 system furnishes explicit horizonless geometries whose degeneracy matches the CFT count, while a 3-charge D1-D5-P state can be similarly realized; fractionation yields light, extended excitations that encode information across macroscopic scales, enabling information to be retrieved in Hawking radiation. This framework resolves the information paradox by introducing macroscopic nonlocal hair and links entropy and radiation rates via AdS/CFT duality. The results suggest that the black hole interior is a complex, horizon-spanning region rather than empty space with a singularity, with implications for dynamics of infall and evaporation and for the nature of quantum gravity.

Abstract

We argue that bound states of branes have a size that is of the same order as the horizon radius of the corresponding black hole. Thus the interior of a black hole is not `empty space with a central singularity', and Hawking radiation can pick up information from the degrees of freedom of the hole.

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 dashed line gives a 'horizon' whose area gives the entropy.