Static and symmetric wormholes respecting energy conditions in Einstein-Gauss-Bonnet gravity

TL;DR

This paper investigates static wormhole solutions in higher-dimensional Einstein-Gauss-Bonnet gravity, classifying solutions based on their relation to general relativity, and identifies conditions under which energy conditions are satisfied or violated.

Contribution

It provides a classification of wormhole solutions in Einstein-Gauss-Bonnet gravity and identifies conditions for energy condition compliance, including explicit solutions in vacuum and dust cases.

Findings

Wormhole throats in the GR branch coincide with branch surfaces and respect energy conditions.

No wormhole solutions exist in the non-GR branch for certain parameter ranges.

Explicit energy-condition-respecting wormhole solutions are found in vacuum and dust cases with specific parameters.

Abstract

Properties of $n(\ge 5)$-dimensional static wormhole solutions are investigated in Einstein-Gauss-Bonnet gravity with or without a cosmological constant $\Lambda$. We assume that the spacetime has symmetries corresponding to the isometries of an $(n-2)$-dimensional maximally symmetric space with the sectional curvature $k=\pm 1, 0$. It is also assumed that the metric is at least $C^{2}$ and the $(n-2)$-dimensional maximally symmetric subspace is compact. Depending on the existence or absence of the general relativistic limit $\alpha \to 0$, solutions are classified into general relativistic (GR) and non-GR branches, respectively, where $\alpha$ is the Gauss-Bonnet coupling constant. We show that a wormhole throat respecting the dominant energy condition coincides with a branch surface in the GR branch, otherwise the null energy condition is violated there. In the non-GR branch, it is shown that there is no wormhole solution for $k\alpha \ge 0$. For the matter field with zero tangential pressure, it is also shown in the non-GR branch with $k\alpha<0$ and $\Lambda \le 0$ that the dominant energy condition holds at the wormhole throat if the radius of the throat satisfies some inequality. In the vacuum case, a fine-tuning of the coupling constants is shown to be necessary and the radius of a wormhole throat is fixed. Explicit wormhole solutions respecting the energy conditions in the whole spacetime are obtained in the vacuum and dust cases with $k=-1$ and $\alpha>0$.