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

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.

💡 Research Summary

The paper investigates whether traversable wormholes can exist in unimodular gravity without violating the null energy condition (NEC). The authors begin by recalling that the Raychaudhuri equation is a purely geometric identity that governs the focusing of geodesic congruences and does not depend on any particular field equations. For a null congruence with tangent vector (k^{a}) (affinely parametrized, twist‑free), the Raychaudhuri equation reads

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