Boundary value problem for black rings

Abstract

We study the boundary value problem for asymptotically flat stationary black ring solutions to the five-dimensional vacuum Einstein equations. Assuming the existence of two additional commuting axial Killing vector fields and the horizon topology of S 1 × S 2 , we show that the only asymptotically flat black ring solution with a regular horizon is the Pomeransky-Sen'kov black ring solution.

Geodesics and symmetries of doubly spinning black rings

“…We might ask whether the unbalanced version [12] of the ring has similar properties. Studying the most general form of the unbalanced metric would be difficult, as it is extremely complicated, but some progress on this question can be made by looking at the limit where the black ring has rotation only in the S 2 direction, as derived by Figueras [26].…”

“…Kunduri, Lucietti and Reall [11] studied the extremal limit and near-horizon geometry of this solution, while Elvang and Rodriguez [5] studied its phase structure, asymptotics and horizon. There is a more general version of the solution, corresponding to an 'unbalanced' ring with conical singularities, which is explicitly presented in [12]. The current literature on this spacetime is reviewed in [9], we give some brief details of its properties in Section 2.…”

More on five dimensional EVH black rings

“…discussions in section 3), if we adjust the expansion around the north pole of the topologically S 2 part of the horizon to be a flat JHEP09(2014)036 R 2 , the expansion around the south pole will show a deficit (or excess) angle and we have a conical disk [8,9]. For the unbalanced rings the mass gets an additional contribution from the pressure (tension) of the conical (defect) disk [5,[7][8][9]. Due to the contribution of this tension the first law of thermodynamics and the Gibbs free energy for unbalanced rings has an extra term which vanishes in the balanced case [8,10].…”

“…In the balanced case constructed and discussed in [2,3], expanding around north and south poles of topologically S 2 part of the horizon we get a 2d flat space without any deficit angle or conical singularity. In a different viewpoint, in the balanced case the centrifugal force from the angular momentum along the ring is tuned to precisely balance off the tension and self-gravitation of the ring [5][6][7]. However, in the unbalanced case [5] (cf.…”

Rotating black rings on Taub-NUT

“…The real breakthrough, however, came with the derivation by Pomeransky and Sen'kov [5] of a black ring rotating in both the S 1 and S 2 directions, and whose S 1 rotation has been tuned to ensure that there is no conical singularity in the space-time. The most general doubly rotating black ring, which in general has a conical singularity, was derived in [6,7].…”