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As I'm sure you are aware the Kretschmann scalar (formed by contracting the contravariant and covariant Riemann tensors) has some use in the identification of gravitational singularities. Specifically, because K is essentially the sum of all permutations of R's components, but is itself coordinate invariant, its divergence at a point is sufficient to prove the existence of a true gravitational singularity at that point.

I am wondering whether this is a necessary condition as well. It seems to me that it is not, since one could imagine a situation in which two terms in the sum diverge in opposite directions. Perhaps I have missed something, though?