Uniqueness theorem for charged dipole rings in five-dimensional minimal supergravity

Abstract

We show a uniqueness theorem for charged dipole rotating black rings in the bosonic sector of five-dimensional minimal supergravity, generalizing our previous work [arXiv:0901.4724] on the uniqueness of charged rotating black holes with topologically spherical horizon in the same theory. More precisely, assuming the existence of two commuting axial Killing vector fields and the same rod structure as the known solutions, we prove that an asymptotically flat, stationary charged rotating black hole with nondegenerate connected event horizon of cross-section topology ${S}^{1}\ifmmode\times\else\texttimes\fi{}{S}^{2}$ in the five-dimensional Einstein-Maxwell-Chern-Simons theory---if exists---is characterized by the mass, charge, two independent angular momenta, dipole charge, and the ratio of the ${S}^{2}$ radius to the ${S}^{1}$ radius. As anticipated, the necessity of specifying dipole charge---which is not a conserved charge---is the new, distinguished ingredient that highlights difference between the present theorem and the corresponding theorem for vacuum case, as well as difference from the case of topologically spherical horizon within the same minimal supergravity. We also consider a similar boundary value problem for other topologically nontrivial black holes within the same theory, and in particular, discuss some nontrivial issues that arise when attempting to generalize the present uniqueness results to include black lenses---provided there exists such a solution in the theory.