Null Raychaudhuri Equation and the Impossibility of Traversable Wormholes in Unimodular Gravity

TL;DR

This paper demonstrates that in unimodular gravity, traversable wormholes cannot exist without violating the null energy condition, due to the invariance of null focusing properties from general relativity.

Contribution

It establishes a local no-go theorem showing traversable wormholes are impossible in unimodular gravity supported by ordinary matter.

Findings

Traversable wormholes violate null energy condition in unimodular gravity.

Null focusing properties are unchanged from general relativity in this framework.

No genuine traversable wormholes supported by ordinary matter exist in unimodular gravity.

Abstract

We formulate the traversability of wormhole throats as a local and covariant null defocusing condition derived from the Raychaudhuri equation. Since unimodular gravity preserves the local geometric structure of spacetime, the null focusing properties of geodesic congruences are unchanged with respect to general relativity. We show that any genuinely traversable wormhole in unimodular gravity necessarily violates the null energy condition, establishing a local no--go theorem for wormholes supported by ordinary matter in this framework.