Fuzzballs and the information paradox: a summary and conjectures

TL;DR

This work argues that the black hole information paradox can be resolved within string theory by replacing the interior with horizon-sized fuzzballs that encode the hole's microstate. By examining explicit constructions in the NS1-P and D1D5 systems, including 2-, 3-, and 4-charge extremal holes and certain non-extremal states, the authors show that microstates have no information-free horizon and can radiate information-bearing quanta, with energy gaps matching CFT predictions. A central message is that the black hole is a highly quantum object with a large phase space of microstates; a collapsing shell can spread over this phase space, yielding unitary evolution and erasing the need for a traditional horizon on relevant timescales. The fuzzball paradigm thus reframes black holes as ensembles of horizonless geometries, with AdS/CFT providing organizing insight for counting states and linking gravity to dual field theory dynamics, potentially shaping broader views on quantum gravity and cosmology.

Abstract

The black hole information paradox is one of the most important issues in theoretical physics. We review some recent progress using string theory in understanding the nature of black hole microstates. For all cases where these microstates have been constructed, one finds that they are horizon sized `fuzzballs'. Most computations are for extremal states, but recently one has been able to study a special family of non-extremal microstates, and see `information carrying radiation' emerge from these gravity solutions. We discuss how the fuzzball picture can resolve the information paradox. We use the nature of fuzzball states to make some conjectures on the dynamical aspects of black holes, observing that the large phase space of fuzzball solutions can make the black hole more `quantum' than assumed in traditional treatments.

Figures (13)

• Figure 1: Constructing a slicing of the black hole geometry. For $r>3GM$ we have the part $S_{out}$ as a $t=constant$ slice. The 'connector' part $S_{con}$ is almost the same on all slices, and has a smooth intrinsic metric as the surface crosses the horizon. The inner part of the slice $S_{in}$ is a $r=constant$ surface, with the value of $r$ kept away from the singularity at $r=0$. The coordinate $\tau$ is only schematic; it will degenerate at the horizon.
• Figure 2: A fourier mode on the initial spacelike surface is evolved to later spacelike surfaces. In the initial part of the evolution the wavelength increases but there is no significant distortion of the general shape of the mode. At this stage the initial vacuum state is still a vacuum state. Further evolution leads to a distorted waveform, which results in particle creation.
• Figure 3: On the initial spacelike slice we have depicted two fourier modes: the longer wavelength mode is drawn with a solid line and the shorter wavelength mode is drawn with a dotted line. The mode with longer wavelength distorts to a nonuniform shape first, and creates an entangled pairs $b_1, c_1$. The mode with shorter wavelength evolves for some more time before suffering the same distortion, and then it creates entangled pairs $b_2, c_2$.
• Figure 4: The infalling matter $Q$ and the entangled pairs $c,b$ shown on the spacelike slices in the Penrose diagram.
• Figure 5: (a) The conventional picture of a black hole (b) the proposed picture -- information of the state is distributed throughout the 'fuzzball'.