A Crinkle in the Wrinkle of Space-time

[Fraser]

Albert Einstein’s revolutionary general theory of relativity describes gravity as a curvature in the fabric of spacetime. Mathematicians at University of California, Davis have come up with a new way to crinkle that fabric while pondering shockwaves. “We show that spacetime cannot be locally flat at a point where two shockwaves collide,” says Blake Temple, [...]

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[Jeff Root]

I would expect the "singularity" to be an artifact of a
numerical simulation. Where two shockwaves meet, the
variables that they are following change more rapidly
than the time intervals they are using. So it looks like
a discontinuity, or singularity.

“We show that spacetime cannot be locally flat at a
point where two shockwaves collide,”

Spacecetime typically isn't locally flat. The presence
of any matter makes it locally non-flat.

-- Jeff, in Minneapolis

[Strange]

I have only skimmed the papers (which are more than somewhat over my head) but it doesn't appear to be (solely) based on simulation. They have an analytical proof as well.

Also, I'm quite sure that anyone performing a numerical simulation would look at issues to do with accuracy and convergence, and adjust the model accordingly.

Spacetime is locally flat, for suitable definitions of "local". I understand this to be equivalent to saying the manifold is differentiable (but I'm sure it is subtler than that). Whereas, in the case they are looking at, it will never be flat however small you make "local"; there is no way of transforming the coordinates between one point and another; it is like a discontinuous function.

[publiusr]

The article ends with these words:

“We wonder whether an exploding stellar shock wave hitting an imploding shock at the leading edge of a collapse, might stimulate stronger than expected gravity waves,” Temple says. “This cannot happen in spherical symmetry, which our theorem assumes, but in principle it could happen if the symmetry were slightly broken.”

Slightly broken with a space probe in the vicinity, say?