Uniqueness theorem for the swirling black ring

Establish whether the uniqueness of the rotating black ring in the five-dimensional swirling background follows from a corresponding uniqueness theorem.

Background

Numerical plots indicate that increasing the swirling parameter or the ring-radius scale can eliminate the non-uniqueness observed for asymptotically flat black rings, leaving one swirling black ring for each relevant parameter value. The authors interpret this as evidence that the swirling background restores uniqueness.

It remains unresolved whether this numerical behavior reflects a general mathematical uniqueness theorem for black rings in the five-dimensional swirling spacetime.

References

The most interesting finding, here, is that the swirling background guarantees the uniqueness of the rotating black ring: one may wonder if this result is related to some uniqueness theorem, as it happens for spherical black holes in four dimensions.

— Black objects in a five-dimensional swirling spacetime  (2609.37511 - Viganò, 29 Sep 2026) in Section 4.2, Mass and angular momentum