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I've been reading through my General Relativity text and the solution for the Schwarzschild problem. I noted a missing piece of how the metric was derived.

Can the metric have discontinuities? I'm reasonably certain it can't be discontinuous, though the Schwarzschild solution shows there can be what I would call a "removable singularity" ie. it can be removed by a choice of coordinates. But could the metric have discontinuities in its derivatives? None of my texts, including my two differential geometry texts, ever seem to mention the question. (Though, perhaps, it could be a an unmentioned lemma of one of the theorems.)

Thanks!

-Dan