  It is an open question whether solutions of the Einstein-Euler equations are
smooth enough to admit locally inertial coordinates at points of shock wave
interaction, or whether "regularity singularities" can exist at such points.
The term {\it regularity singularity} was proposed by the authors as a point in
spacetime 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 arbitrary
interactions has been proven for the Einstein-Euler equations in spherically
symmetric spacetimes, but $C^{1,1}$ is the requisite smoothness required for
space-time to be locally flat. Thus the open problem of regularity
singularities is the problem as to whether locally inertial coordinate systems
exist at shock waves within the larger $C^{1,1}$ atlas. To clarify this open
problem, 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 can
never be made to vanish within the atlas of {\it smooth} coordinate
transformations, the atlas usually assumed in classical differential geometry.
Thus the problem of existence of regularity singularities is equivalent to the
question as to whether or not these Coriolis type effects are essentially
non-removable and `real', or merely coordinate effects that can be removed, (in
analogy to classical Coriolis forces), by going to the less regular atlas of
$C^{1,1}$ transformations. If essentially non-removable, it would argue
strongly for a `real' new physical effect for General Relativity, providing a
physical context to the open problem of regularity singularities.
