We construct the first family of horizonless supergravity solutions that have the same mass, charges, and angular momenta as general supersymmetric rotating D1-D5-P black holes in five dimensions. This family includes solutions with arbitrarily small angular momenta, deep within the regime of quantum numbers and couplings for which a large classical black hole exists. These geometries are well approximated by the black-hole solution, and in particular exhibit the same near-horizon throat. Deep in this throat, the black-hole singularity is resolved into a smooth cap. We also identify the holographically dual states in the N=(4,4) D1-D5 orbifold conformal field theory (CFT). Our solutions are among the states counted by the CFT elliptic genus, and provide examples of smooth microstate geometries within the ensemble of supersymmetric black-hole microstates.

Abstract:We construct an infinite family of smooth asymptotically-flat supergravity solutions that have the same charges and angular momenta as general supersymmetric D1-D5-P black holes, but have no horizon. These solutions resemble the corresponding black hole to arbitrary accuracy outside of the horizon: they have asymptotically flat regions, AdS 3 × S 3 throats and very-near-horizon AdS 2 throats, which however end in a smooth cap rather than an event horizon. The angular momenta of the solutions are general, and in particular can take arbitrarily small values. Upon taking the AdS 3 × S 3 decoupling limit, we identify the holographically-dual CFT states.

The geometries describing D1-D5-P bound states in string theory have three regions: flat asymptotics, an anti-de Sitter throat, and a 'cap' region at the bottom of the throat. We identify the CFT description of a known class of supersymmetric D1-D5-P microstate geometries which describe degrees of freedom in the cap region. The class includes both regular solutions and solutions with conical defects, and generalizes configurations with known CFT descriptions: a parameter related to spectral flow in the CFT is generalized from integer to fractional values. We provide strong evidence for this identification by comparing the massless scalar excitation spectrum between gravity and CFT and finding exact agreement

Superstrata are bound states in string theory that carry D1, D5, and momentum charges, and whose supergravity descriptions are parameterized by arbitrary functions of (at least) two variables. In the D1-D5 CFT, typical threecharge states reside in high-degree twisted sectors, and their momentum charge is carried by modes that individually have fractional momentum. Understanding this momentum fractionation holographically is crucial for understanding typical black-hole microstates in this system. We use solution-generating techniques to add momentum to a multi-wound supertube and thereby construct the first examples of asymptotically-flat superstrata. The resulting supergravity solutions are horizonless and smooth up to well-understood orbifold singularities. Upon taking the AdS 3 decoupling limit, our solutions are dual to CFT states with momentum fractionation. We give a precise proposal for these dual CFT states. Our construction establishes the very nontrivial fact that large classes of CFT states with momentum fractionation can be realized in the bulk as smooth horizonless supergravity solutions. 7 Our spherical bipolar angles ϕ1 and ϕ2 are related to those of [19] by ϕ here 1 = φ there , ϕ here 2 = ψ there .

We explore the stringy structure of 1/2-BPS bound states of NS fivebranes carrying momentum or fundamental string charge, in the decoupling limits leading to little string theory and to AdS3/CFT2 duality. We develop an exact worldsheet description of these states using null-gauged sigma models, and illustrate the construction by deriving the closed-form solution sourced by an elliptical NS5-F1 supertube. The Calabi-Yau/Landau-Ginsburg correspondence maps this geometrical worldsheet description to a non-compact LG model whose superpotential is determined by the fivebrane source configuration. Singular limits of the 1/2-BPS configuration space result when the fivebrane worldvolume self-intersects, as can be seen from both sides of the CY/LG duality — on the Landau-Ginsburg side from the degeneration of the superpotential(s), and on the geometrical side from an analysis of D-brane probes. These singular limits are a portal to black hole formation via the condensation of the branes that are becoming massless, and thus exhibit in the gravitational bulk description the central actors in the non-gravitational dual theory underlying black hole thermodynamics.

Non-supersymmetric black hole microstates are of great interest in the context of the black hole information paradox. We identify the holographic description of the general class of non-supersymmetric orbifolded D1-D5-P supergravity solutions found by Jejjala, Madden, Ross and Titchener. This class includes both completely smooth solutions and solutions with conical defects, and in the near-decoupling limit these solutions describe degrees of freedom in the cap region. The CFT description involves a general class of states obtained by fractional spectral flow in both left-moving and right-moving sectors, generalizing previous work which studied special cases in this class. We compute the massless scalar emission spectrum and emission rates in both gravity and CFT and find perfect agreement, thereby providing strong evidence for our proposed identification. We also investigate the physics of ergoregion emission as pair creation for these orbifolded solutions. Our results represent the largest class of non-supersymmetric black hole microstate geometries with identified CFT duals presently known

We examine some recently-constructed families of asymptotically-AdS 3 × S 3 supergravity solutions that have the same charges and mass as supersymmetric D1-D5-P black holes, but that cap off smoothly with no horizon. These solutions, known as superstrata, are quite complicated, however we show that, for an infinite family of solutions, the null geodesic problem is completely integrable, due to the existence of a non-trivial conformal Killing tensor that provides a quadratic conservation law for null geodesics. This implies that the massless scalar wave equation is separable. For another infinite family of solutions, we find that there is a non-trivial conformal Killing tensor only when the left-moving angular momentum of the massless scalar is zero. We also show that, for both these families, the metric degrees of freedom have the form they would take if they arose from a consistent truncation on S 3 down to a (2 + 1)-dimensional space-time. We discuss some of the broader consequences of these special properties for the physics of these black-hole microstate geometries.

Abstract:We comment on a recent paper of Almheiri, Marolf, Polchinski and Sully who argue against black hole complementarity based on the claim that an infalling observer 'burns' as he attempts to cross the horizon. We show that measurements made by an infalling observer outside the horizon are statistically identical for the cases of vacuum at the horizon and radiation emerging from a stretched horizon. This forces us to follow the dynamics all the way to the horizon, where we need to know the details of Planck-scale physics. We note that in string theory the fuzzball structure of microstates does not give any place to 'continue through' this Planck regime. AMPS argue that interactions near the horizon preclude traditional complementarity. But the conjecture of 'fuzzball complementarity' works in the opposite way: the infalling quantum is absorbed by the fuzzball surface, and it is the resulting dynamics that is conjectured to admit a complementary description.