Higher Dimensional Wormhole Geometries with Compact Dimensions

TL;DR

This paper explores higher-dimensional wormhole solutions in Einstein gravity with compact dimensions, revealing how extra dimensions influence the classical vacuum structure and energy conditions, especially in dynamic scenarios.

Contribution

It introduces a new gauge for studying wormhole throats in higher dimensions and analyzes the impact of extra dimensions on energy conditions and vacuum structure.

Findings

In static cases, the size of WEC-respecting throats is dimension-dependent.

At D=5, restrictions on the throat size are eliminated.

Time dependence tends to violate the WEC at the wormhole throat.

Abstract

This paper studies wormhole solutions to Einstein gravity with an arbitrary number of time dependent compact dimensions and a matter-vacuum boundary. A new gauge is utilized which is particularly suited for studies of the wormhole throat. The solutions possess arbitrary functions which allow for the description of infinitely many wormhole systems of this type and, at the stellar boundary, the matter field is smoothly joined to vacuum. It turns out that the classical vacuum structure differs considerably from the four dimensional theory and is therefore studied in detail. The presence of the vacuum-matter boundary and extra dimensions places interesting restrictions on the wormhole. For example, in the static case, the radial size of a weak energy condition (WEC) respecting throat is restricted by the extra dimensions. There is a critical dimension, D=5, where this restriction is eliminated. In the time dependent case, one \emph{cannot} respect the WEC at the throat as the time dependence actually tends the solution towards WEC violation. This differs considerably from the static case and the four dimensional case.