Towards higher dimensional black rings

TL;DR

This paper investigates the challenges in finding higher-dimensional black ring solutions, revealing symmetry constraints and constructing supersymmetric solutions that lack regular horizons, thus advancing understanding of higher-dimensional black objects.

Contribution

It clarifies why exact higher-dimensional black ring solutions are difficult to obtain and constructs supersymmetric solutions with similar symmetries that lack regular horizons.

Findings

Separable base symmetry cannot occur above five dimensions.

Supersymmetric solutions with 5D black ring symmetries lack regular horizons.

Identifies fundamental symmetry limitations in higher-dimensional black rings.

Abstract

Despite all attempts, exact solutions for black rings in more than five dimensions remain elusive. In this paper we clarify some of the reasons for that, in particular we show that a peculiar symmetry of the five--dimensional black ring - separability of the base - cannot occur in dimensions higher than five. We also construct supersymmetric solutions that have symmetries of 5D supersymmetric black ring and show that they do not have regular horizons.