The fuzzball nature of two-charge black hole microstates

Abstract

It has been suggested by A. Sen that the entropy of two-charge supersymmetric bound states in string theory should be accounted for by adding the entropy of source-free horizonless supergravity solutions to the entropy associated with the horizons of small black holes. This would imply that the entropy arises differently depending on the duality frame: in the D1-D5 frame one would count source-free horizonless solutions, while in the NS1-P frame one would compute the area of a horizon. This might lead to the belief that the microstates are described by fuzzball solutions in the D1-D5 duality frame but by a black hole with a horizon in the latter. We argue that this is not the case, and that the microstates are fuzzballs in all duality frames. We observe that the scaling argument used by Sen fails to account for the entropy in the D1-P and other duality frames. We also note that the traditional extremal black hole solution is not a complete string background, since finite-action paths connect the exterior near-horizon extremal throat to the region inside the horizon, including the singularity. The singularity of the traditional black hole solution does not give a valid boundary condition for a fundamental string; correcting this condition by resolving the singularity modifies the black hole to a fuzzball with no horizon. We argue that for questions of counting states, the traditional black hole solution should be understood through its Euclidean continuation as a saddle point, and that the Lorentzian states being counted are fuzzballs in all duality frames. arXiv:1811.09647v1 [hep-th]

Stringy structure at the BPS bound

“…Classically, there is a continuous moduli space of BPS states characterized by the arbitrary choice of source profile F(ṽ), whose Fourier modes are the coherent state parameters; quantum mechanically, the underlying basis states (2.8) comprise a discretuum of exp[2π √ 2n 1 n 5 ] states [25] (see also [26]). The explicit description of this exponential number of states in the bulk has been interpreted as resolving the singularity of a string-sized black hole at the correspondence point and demonstrating the absence of a horizon in the microscopic bulk description [3,5], though this interpretation remains a matter of debate [9,27].…”

“…The general family of supergravity solutions describing 1/2-BPS states in the NS5-P and other duality frames was constructed and studied in [2][3][4][5][6][7] (see also [8,9]). We review their properties in section 2, focusing on solutions with pure NS-NS flux.…”

Little strings, long strings, and fuzzballs

“…There has been some debate as to how one should interpret the two-charge solutions, in particular how the entropy of the system arises in different duality frames (see [37] for a recent discussion and further references). The fuzzball paradigm was to some extent motivated by the idea that these two-charge solutions and the fact that they cap off without a horizon might be a good model for what happens when one adds a third charge to obtain a large black hole.…”

AdS3 holography at dimension two

“…Nevertheless, by approaching typical microstates through limits of progressively less atypical microstates which are amenable to study, one hopes to gain valuable insights about the structure of typical states. For a recent discussion of related points, see [23].…”