Vacuum solutions with nontrivial boundaries for the Einstein-Gauss-Bonnet theory

TL;DR

This paper classifies static vacuum solutions in Einstein-Gauss-Bonnet gravity with nontrivial boundary geometries, revealing new black hole and wormhole solutions under specific coupling conditions.

Contribution

It provides a classification of static solutions with warped product metrics, identifying conditions for boundary geometry relaxation and discovering new black hole and wormhole solutions.

Findings

Existence of three main geometric branches in the bulk.

New black hole solutions in vacuum.

Wormhole solutions enabled by boundary conditions.

Abstract

The classification of certain class of static solutions for the Einstein-Gauss-Bonnet theory in vacuum is presented. The spacelike section of the class of metrics under consideration is a warped product of the real line with a nontrivial base manifold. For arbitrary values of the Gauss-Bonnet coupling, the base manifold must be Einstein with an additional scalar restriction. The geometry of the boundary can be relaxed only when the Gauss-Bonnet coupling is related with the cosmological and Newton constants, so that the theory admits a unique maximally symmetric solution. This additional freedom in the boundary metric allows the existence of three main branches of geometries in the bulk, containing new black holes and wormholes in vacuum.