Wormhole geometries in fourth-order conformal Weyl gravity

TL;DR

This paper explores wormhole geometries within fourth-order conformal Weyl gravity, showing that certain configurations can satisfy key energy conditions, potentially making traversable wormholes feasible without exotic matter.

Contribution

It demonstrates that specific wormhole solutions in conformal Weyl gravity can meet energy conditions, unlike in standard general relativity, suggesting more physically plausible traversable wormholes.

Findings

Some wormhole solutions satisfy the null energy condition.

Effective superluminal motion remains possible in these geometries.

Certain configurations do not require exotic matter at the throat.

Abstract

We present an analysis of the classic wormhole geometries based on conformal Weyl gravity, rather than standard general relativity. The main characteristics of the resulting traversable wormholes remain the same as in the seminal study by Morris and Thorne, namely, that effective super-luminal motion is a viable consequence of the metric. Improving on previous work on the subject, we show that for particular choices of the shape and redshift functions the wormhole metric in the context of conformal gravity does not violate the main energy conditions at or near the wormhole throat. Some exotic matter might still be needed at the junction between our solutions and flat spacetime, but we demonstrate that the averaged null energy condition (as evaluated along radial null geodesics) is satisfied for a particular set of wormhole geometries. Therefore, if fourth-order conformal Weyl gravity is a correct extension of general relativity, traversable wormholes might become a realistic solution for interstellar travel.