A Critique of the Fuzzball Program

TL;DR

This paper critically examines the fuzzball proposal for black hole microstates, arguing that quantum fluctuations undermine their viability and they are unlikely to resolve the black hole information paradox.

Contribution

It provides a detailed analysis showing that typical fuzzball geometries differ insignificantly from black holes at the horizon scale and are unreliable due to large quantum fluctuations.

Findings

Fuzzball geometries only differ significantly from black holes at Planck-scale distances.

Quantum fluctuations in fuzzball geometries are large, making them unreliable.

Certain fuzzball solutions violate expected energy gap properties.

Abstract

We explore the viability of fuzzballs as candidate microstate geometries for the black hole, and their possible role in resolutions of the information paradox. We argue that if fuzzballs provide a description of black-hole microstates, then the typical fuzzball geometry can only differ significantly from the conventional black-hole geometry at a Planck-scale-distance from the horizon. However, precisely in this region, quantum fluctuations in the fuzzball geometry become large and the fuzzball geometry becomes unreliable. We verify these expectations through a detailed calculation of quantum expectation values and quantum fluctuations in the two-charge fuzzball geometries. We then examine some of the solutions discovered in arXiv:1607.03908. We show, based on a calculation of a probe two-point function in this background, that these solutions, and others in their class, violate robust expectations about the gap in energies between successive energy eigenstates, and differ too much from the conventional black hole to represent viable microstates. We conclude that while fuzzballs are interesting star-like solutions in string theory, they do not appear to be relevant for resolving the information paradox, and cannot be used to make valid inferences about black-hole interiors.