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We show that the regularity of the gravitational metric tensor in sphericallysymmetric spacetimes cannot be lifted from $C^{0,1}$ to $C^{1,1}$ within theclass of $C^{1,1}$ coordinate transformations in a neighborhood of a point ofshock wave interaction in General Relativity, without forcing the determinantof the metric tensor to vanish at the point of interaction. This is in contrastto Israel's Theorem which states that such coordinate transformations alwaysexist in a neighborhood of a point on a smooth single shock surface. Theresults thus imply that points of shock wave interaction represent a new kindof singularity for perfect fluids evolving in spacetime, singularities thatmake perfectly good sense physically, that can form from the evolution ofsmooth initial data, but at which the spacetime is not locally Minkowskianunder any coordinate transformation. In particular, at such singularities,delta function sources in the second derivatives of the gravitational metrictensor exist in all coordinate systems of the $C^{1,1}$ atlas, but due tocancelation, the curvature tensor remains uniformly bounded.

Points of General Relativisitic Shock Wave Interaction are "Regularity Singularities" where Spacetime is Not Locally Flat