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

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 ${\alpha }^{\prime }$. Moreover, in the limit of large ring radius, the suitably rescaled black ring maximal value of ${\alpha }^{\prime }$ and the black string maximal value of ${\alpha }^{\prime }$ agree.

43 pages, 14 figures

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