A covariant Moore-Penrose algorithm for complex degenerate metrics is formulated, but its uniqueness and torsion interpretation depend on an arbitrary auxiliary metric and the central proof is incomplete.
Skyrmion spacetime defect
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abstract
A finite-energy static classical solution is obtained for standard Einstein gravity coupled to an $SO(3)\times SO(3)$ chiral model of scalars [a Skyrme model]. This nonsingular localized solution has nontrivial topology for both the spacetime manifold and the $SO(3)$ matter fields. The solution corresponds to a single spacetime defect embedded in flat Minkowski spacetime.
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Complex degenerate metrics in general relativity: a covariant extension of the Moore-Penrose algorithm
A covariant Moore-Penrose algorithm for complex degenerate metrics is formulated, but its uniqueness and torsion interpretation depend on an arbitrary auxiliary metric and the central proof is incomplete.