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

TL;DR

Problem: whether unimodular gravity (UG) allows traversable wormholes supported by matter obeying the null energy condition (NEC). Approach: formulate traversability via the local null Raychaudhuri equation and flare-out at the throat, using the fact UG shares the same geometric structure as GR. Findings: the null Raychaudhuri equation is unchanged in UG; at the throat, $R_{ab}k^a k^b<0$ implies $T_{ab}k^a k^b<0$, i.e. NEC must be violated for ordinary matter, yielding a local no-go theorem for traversable wormholes in UG. Implications: UG does not evade the standard obstruction to traversable wormholes; claims of NEC-preserving traversables in UG require nonlocal reinterpretations or abandoning the covariant traversability criterion.

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.