Bubbling Supertubes and Foaming Black Holes

We construct smooth BPS three-charge geometries that resolve the zero-entropy singularity of the U(1) x U(1) invariant black ring. This singularity is resolved by a geometric transition that results in geometries without any branes sources or singularities but with non-trivial topology. These geometries are both ground states of the black ring, and non-trivial microstates of the D1-D5-P system. We also find the form of the geometries that result from the geometric transition of N zero-entropy black rings, and argue that, in general, such geometries give a very large number of smooth bound-state three-charge solutions, parameterized by 6N functions. The generic microstate solution is specified by a four-dimensional hyper-Kahler geometry of a certain signature, and contains a ``foam'' of non-trivial two-spheres. We conjecture that these geometries will account for a significant part of the entropy of the D1-D5-P black hole, and that Mathur's conjecture might reduce to counting certain hyper-Kahler manifolds.Comment: 40 pages, harvmac. v2 references added, typo correcte

Supersymmetric black rings and three-charge supertubes

We present supergravity solutions for 1/8-supersymmetric black supertubes with three charges and three dipoles. Their reduction to five dimensions yields supersymmetric black rings with regular horizons and two independent angular momenta. The general solution contains seven independent parameters and provides the first example of non-uniqueness of supersymmetric black holes. In ten dimensions, the solutions can be realized as D1-D5-P black supertubes. We also present a worldvolume construction of a supertube that exhibits three dipoles explicitly. This description allows an arbitrary cross-section but captures only one of the angular momenta.Comment: 59 pages, 6 figures; v2: minor correction

Large D gravity and charged membrane dynamics with nonzero cosmological constant

In this paper, we have found a class of dynamical charged 'black-hole' solutions to Einstein-Maxwell system with a non-zero cosmological constant in a large number of spacetime dimensions. We have solved up to the first sub-leading order using large D scheme where the inverse of the number of dimensions serves as the perturbation parameter. The system is dual to a dynamical membrane with a charge and a velocity field, living on it. The dual membrane has to be embedded in a background geometry that itself, satisfies the pure gravity equation in presence of a cosmological constant. Pure AdS / dS are particular examples of such background. We have also obtained the membrane equations governing the dynamics of the charged membrane. The consistency of our membrane equations is checked by calculating the quasi-normal modes with different Einstein-Maxwell systems in AdS/dS.Comment: 63 pages, v3: appendix added, Accepted for publication in JHE

Bubbles on Manifolds with a U(1) Isometry

We investigate the construction of five-dimensional, three-charge supergravity solutions that only have a rotational U(1) isometry. We show that such solutions can be obtained as warped compactifications with a singular ambi-polar hyper-Kahler base space and singular warp factors. We show that the complete solution is regular around the critical surface of the ambi-polar base. We illustrate this by presenting the explicit form of the most general supersymmetric solutions that can be obtained from an Atiyah-Hitchin base space and its ambi-polar generalizations. We make a parallel analysis using an ambi-polar generalization of the Eguchi-Hanson base space metric. We also show how the bubbling procedure applied to the ambi-polar Eguchi-Hanson metric can convert it to a global AdS_2xS^3 compactification.Comment: 33 pages, 5 figures, LaTeX; references adde