Visser defines some class of wormholes with polyhedral mouthes, as a limit of smoothed polyhedrons as the radius of the edges go to zero. Does this limit actually make sense, as an actual spacetime? That is, can I remove two polyhedrons from Minkowski space and identify them in a way that makes sense as a Lorentzian manifold? I've got some doubts due to the following issues :
- Gluing together manifolds require a collared neighbourhood around the manifold edges, which I'm not sure exist if the edge isn't smooth (this isn't even a manifold with boundaries, it's a manifold with corners)
- If such a gluing can be performed, I don't think the resulting manifold is even $C^1$
- It's a theorem that metrics of the Geroch-Traschen class cannot be generated by linear densities, only by surface densities, meaning that it could only be described by Colombeaux algebras in GR
So can such a spacetime be constructed, or should it just be considered by some very small radii of the edges and corners?
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