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Dec 4, 2016 at 8:38 comment added Julian Moore I also note that your points should carry through to more general spacetimes where the metric is smooth except for a surface of discontinuity as described.
Dec 4, 2016 at 8:33 vote accept Julian Moore
Dec 4, 2016 at 8:33 comment added Julian Moore Thank you. (a) was my intuition, but what may be "trivial" is absolutely dependent on knowing you know the correct approach - thanks for being definitive ;) (b) The Christoffel issue generally I had considered, but not from the $\gamma(t) \in \Sigma$ not discretem geodesic equation at $\Sigma$ case - except for being distracted by null sections. I don't follow the weak formulation concept, but insofar as the answer remains -ve I'm content.
Dec 1, 2016 at 9:51 history answered Matthias Ludewig CC BY-SA 3.0