Static solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory in vacuum

TL;DR

This paper classifies static vacuum solutions in Einstein-Gauss-Bonnet gravity for dimensions five and higher, revealing conditions on boundary geometries and discovering new black hole and wormhole solutions.

Contribution

It provides a classification of static solutions with nontrivial boundaries in Einstein-Gauss-Bonnet theory, highlighting the role of boundary geometry and special coupling cases.

Findings

Boundary must be Einstein for generic Gauss-Bonnet coupling

In special coupling cases, boundary geometry is more flexible

Discovered new black hole and wormhole solutions in vacuum

Abstract

The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is performed in $d\geq5$ dimensions. The class of metrics under consideration is such that the spacelike section is a warped product of the real line and an arbitrary base manifold. It is shown that for a generic value of the Gauss-Bonnet coupling, the base manifold must be necessarily Einstein, with an additional restriction on its Weyl tensor for $d>5$. The boundary admits a wider class of geometries only in the special case when the Gauss-Bonnet coupling is such that the theory admits a unique maximally symmetric solution. The additional freedom in the boundary metric enlarges the class of allowed geometries in the bulk, which are classified within three main branches, containing new black holes and wormholes in vacuum.