One ring to rule them all and in the darkness bind them?

Abstract

We construct all eleven-dimensional, three-charge BPS solutions that preserve a fixed, standard set of supersymmetries. Our solutions include all BPS three-charge rotating black holes, black rings, supertubes, as well as arbitrary superpositions of these objects. We find very large families of black rings and supertubes with profiles that follow arbitrary closed curves in the spatial R 4 transverse to the branes. The black rings copiously violate black hole uniqueness. The supertube solutions are completely regular, and generically have small curvature. They also have the same asymptotics as the three-charge black hole; and so they might be mapped to microstates of the D1-D5-p system and used to explain the entropy of this black hole.

Three-charge supertubes in a rotating black hole background

“…The subject of supersymmetric black rings in the presence of a BMPV black hole was treated in [6] and the issue of adiabatic mergers of the ring with the black hole appeared in [22,23]. The authors, using the same embedding as presented here, found an exact BPS supergravity solution for the eleven dimensional lift of the black ring + black hole system; this solution can also be expressed in terms of Type IIA or IIB supergravity.…”

“…There is another supertube for this background whose supersymmetric limit has {F zσ < 0, j 1 < 0, j 2 < 0}. 6 Unlike the other charges, q F 1 has a value that in general depends on the black hole charges, as well as the position and velocity of the supertube, as we will see in section 5. Its form in a BPS configuration is 17) where V 6 is the full spatial six-volume (2π) 6 R z 4 .…”

“…Recent work, e.g. [5][6][7][8][9], has shown that supergravity supertubes are part of a larger class of solutions of supergravity, called black supertubes, that saturate a Bogomol'nyi-Prasad-Sommerfeld (BPS) bound. These supersymmetric solutions in general possess three charges, three dipole moments, two independent angular momenta and an event horizon.…”

“…(3.6) shows that a single D6-brane tube is inappropriate for such a task. Consequently, we construct the supertube out of an even number k of coincident D6-branes that are expected [6,10] to form a marginally bound state. 4 (This is done with the understanding that k is small enough for the DBI approximation to hold, which implies g s k 1.)…”

More rings to rule them all: fragmentation, 4D↔ 5Dand split-spectral flows

“…Of course the multi-rings that we generate in this note by these methods, are by no means any new solutions which had previously been unheard of. For that matter, we point to some of the extensive literature, where several classes of 5D multi-center solutions have been worked out : [19], [24], [25], [26], [27]. The focus in this note is based more in the spirit of the box diagram in eq.…”