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It is an open question whether solutions of the Einstein-Euler equations aresmooth enough to admit locally inertial coordinates at points of shock waveinteraction, or whether "regularity singularities" can exist at such points.The term {\it regularity singularity} was proposed by the authors as a point inspacetime where the gravitational metric tensor is Lipschitz continuous($C^{0,1}$), but no smoother, in any coordinate system of the $C^{1,1}$ atlas.An existence theory for shock wave solutions in $C^{0,1}$ admitting arbitraryinteractions has been proven for the Einstein-Euler equations in sphericallysymmetric spacetimes, but $C^{1,1}$ is the requisite smoothness required forspace-time to be locally flat. Thus the open problem of regularitysingularities is the problem as to whether locally inertial coordinate systemsexist at shock waves within the larger $C^{1,1}$ atlas. To clarify this openproblem, we identify new "Coriolis type" effects in the geometry of $C^{0,1}$shock wave metrics and prove they are essential in the sense that they cannever be made to vanish within the atlas of {\it smooth} coordinatetransformations, the atlas usually assumed in classical differential geometry.Thus the problem of existence of regularity singularities is equivalent to thequestion as to whether or not these Coriolis type effects are essentiallynon-removable and `real', or merely coordinate effects that can be removed, (inanalogy to classical Coriolis forces), by going to the less regular atlas of$C^{1,1}$ transformations. If essentially non-removable, it would arguestrongly for a `real' new physical effect for General Relativity, providing aphysical context to the open problem of regularity singularities.

"Regularity Singularities" and the Scattering of Gravity Waves in Approximate Locally Inertial Frames