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 ${\mathrm{S}}^{1}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{2}$, we show that the only asymptotically flat black ring solution with a regular horizon is the Pomeransky-Sen'kov black ring solution.