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.
Highlights
In higher-dimensional supergravities, it is sometimes possible to find horizonless solutions, called fuzzballs, with the same charges as a black hole
The fuzzball program is the bold idea that such geometries can be used to parametrize the set of microstates in quantum gravity that correspond to a black hole
The fuzzball program suggests that the black hole should be viewed only as some kind of “average” geometry, with individual microstates specified by distinct horizonless geometries
Summary
In higher-dimensional supergravities, it is sometimes possible to find horizonless solutions, called fuzzballs, with the same charges as a black hole. Given the considerable effort that continues to be directed toward understanding fuzzballs, we believe it is pertinent to address the following question: is it consistent with the principles of statistical mechanics to expect that black-hole microstates can be represented by distinct geometries, which can be analyzed by studying classical solutions?. We consider the weaker possibility that, while fuzzballs might not provide a useful representation of typical states, they might still provide a basis that spans all black-hole microstates In this context, we prove some simple bounds on how atypical basis elements can be. IV, we analyze the recently discovered class of asymptotically anti-de Sitter (AdS) solutions that correspond to 1=4-BPS states in the D1–D5 system [10] Such 1=4-BPS states are described by a black hole with finite horizon area [11], but the geometries of Ref.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
