We explore the role of differential invariants on the regularity of spacetime. Specifically, we consider spherically symmetric, static spacetimes, which have regular curvature invariants at the origin, but a diverging higher-order differential invariant. Exact `solutions' which meet this criterion and satisfy all energy conditions are constructed. We then examine the physical source of the divergence in the differential invariants and conclude by showing that the singularities are weak.
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Musgrave et al. (1995) studied this question.
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