Can wormhole spacetimes in Unimodular Gravity be supported by ordinary matter? A general proof of the exotic matter requirement

TL;DR

This paper proves that traversable wormholes in Unimodular Gravity inherently require exotic matter due to geometric constraints, similar to General Relativity.

Contribution

It provides a general no-go theorem showing the necessity of exotic matter in all traversable wormholes within Unimodular Gravity, independent of specific configurations.

Findings

All traversable wormholes in Unimodular Gravity violate the Null Energy Condition.

The geometric flaring-out condition implies the need for exotic matter.

This requirement is fundamental and not dependent on particular solution choices.

Abstract

We establish a general no--go theorem demonstrating that all traversable wormhole configurations in Unimodular Gravity necessarily require exotic matter. The proof relies solely on the geometric flaring-out condition, $b'(r_0) \leq 1$, which directly implies that $\rho(r_0) + p_r(r_0) \leq 0$ at the throat. This condition represents a violation of the Null Energy Condition and, consequently, of the Weak and Strong Energy Conditions, independently of the particular choice of shape function, redshift function, or equation of state. This result holds for both tidal and zero-tidal-force configurations, showing that the requirement of exotic matter is a fundamental geometric consequence of the traversability condition rather than an artifact of specific solution choices. Therefore, Unimodular Gravity shares this fundamental constraint with General Relativity.