Generalized Weyl solutions in d=5 Einstein-Gauss-Bonnet theory: the static black ring

TL;DR

This paper extends the construction of static axisymmetric solutions to Einstein-Gauss-Bonnet gravity in five dimensions and provides numerical evidence for the existence of static black rings, highlighting the impact of the Gauss-Bonnet term.

Contribution

It generalizes Weyl coordinates and rod-structure to Einstein-Gauss-Bonnet theory and demonstrates the existence of static black rings in this context.

Findings

Static black rings exist in Einstein-Gauss-Bonnet theory in five dimensions.

The Gauss-Bonnet term reduces the conical excess of black rings.

Black rings exist up to a maximum Gauss-Bonnet coupling, which matches the black string limit at large radius.

Abstract

We argue that the Weyl coordinates and the rod-structure employed to construct static axisymmetric solutions in higher dimensional Einstein gravity can be generalized to the Einstein-Gauss-Bonnet theory. As a concrete application of the general formalism, we present numerical evidence for the existence of static black ring solutions in Einstein-Gauss-Bonnet theory in five spacetime dimensions. They approach asymptotically the Minkowski background and are supported against collapse by a conical singularity in the form of a disk. An interesting feature of these solutions is that the Gauss-Bonnet term reduces the conical excess of the static black rings. Analogous to the Einstein-Gauss-Bonnet black strings, for a given mass the static black rings exist up to a maximal value of the Gauss-Bonnet coupling constant $\alpha'$. Moreover, in the limit of large ring radius, the suitably rescaled black ring maximal value of $\alpha'$ and the black string maximal value of $\alpha'$ agree.