All traversable wormholes in Unimodular Gravity require exotic matter because the flaring-out condition at the throat forces a violation of the null energy condition, independent of shape, redshift, or equation of state.
Visser, Lorentzian Wormholes: from Einstein to Hawking (AIP Press, New York, USA, 1996) https:// link.springer.com/book/9781563966538
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Can wormhole spacetimes in Unimodular Gravity be supported by ordinary matter? A general proof of the exotic matter requirement
All traversable wormholes in Unimodular Gravity require exotic matter because the flaring-out condition at the throat forces a violation of the null energy condition, independent of shape, redshift, or equation of state.