Almost everyone wrongly assumes that the Earth's mantle is liquid, but it isn't (only the outer core is). Is it possible then that there are hollow spaces within the mantle, similar to caves in the crust? What could they look like and up to how much of the mantle could be hollow? What might be inside mantle caverns? Would they be filled with gas or rather vacuum?
It is extremely unlikely that any hollow volumes exist in the mantle.
The mantle is a convecting solid which can deform over long timescales. Let's assume that such a cavern did somehow form. Whatever it is filled it, would be of lower density than the surrounding rock. It would slowly rise upwards through the solid-yet-deformable mantle until it reaches a place where the rocks are brittle, not ductile. That place is the crust. And as you know, the crust is full of caverns and there is no problem with that.