I'm wondering if the possibility of existence of stable spacetime topological defects has ever been explored in the literature. As an example one can consider smth like propagation in time of a handle attached to a two-dimensional space. If these were small, such defects could be treated as particles, if large — as regions of spacetime interacting along their boundaries.
Again, what I mean is a rather compact unfoldable object, not just a domain-wall solution (the latter implies different asymptotics at infinities and could correspond to studies the borders between the former).
Obviously, the effects of such configurations on matter would be of huge interest.