I would guess that that would depend on the situation. I would think that whatever method you have of moving a mouth of the wormhole, would have some interacti

I would guess that that would depend on the situation. I would think that whatever method you have of moving a mouth of the wormhole, would have some interactions with the masses providing the gravitation. Also, I'm not 100% sure that a wormhole would not have something like an inherent mass, because iirc there are solutions where a black hole mass is entirely because of the way spacetime is set up, without any particles needed? I'm not sure about that, but I think that is what I read..