A gravitational model for a matter-free torsion ball

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Abstract
A classical model of a gravitational field is constructed in terms of two distinct geometries. It is formulated in terms of a purely geometric action with distinct densities in different space-time domains. An explicit state spherically symmetric solution for each geometry is found and matching properties across a world tube generated by a closed space-like submanifold are discussed in terms of the associated second fundamental forms. The interior geometry has bounded curvature and torsion. The exterior region has a Schwarzschild geometry. The model simulates distinct phases of the gravitational field and is motivated by E. Cartan's (1922) analogy of torsion effects with dislocation phenomena in continuum mechanics.