Math Shows How Shockwaves Could Crinkle Space

Mathematicians at UC Davis have come up with a new way to crinkle up the fabric of space-time -- at least in theory.

"We show that space-time cannot be locally flat at a point where two shock waves collide," said Blake Temple, professor of mathematics at UC Davis. "This is a new kind of singularity in general relativity."

Temple and his collaborators study the mathematics of how shockwaves in a perfect fluid can affect the curvature of space-time in general relativity. A singularity is a patch of space-time that cannot be made to look flat in any coordinate system, Temple said. One example of a singularity is inside a black hole, where the curvature of space becomes extreme. The results are reported in two papers by Temple with graduate students Moritz Reintjes and Zeke Vogler, respectively, both published in the journal Proceedings of the Royal Society A. In earlier work, Temple and collaborator Joel Smoller, Lamberto Cesari professor of mathematics at the University of Michigan, produced a model for the biggest shockwave of all, created from the Big Bang when the universe burst into existence But the theory starts from the assumption that any local patch of space-time looks flat, Temple said. Einstein's theory of general relativity explains gravity as a curvature in space-time.

Vogler's doctoral work used mathematics to simulate two shockwaves colliding, while Reintjes followed up with an analysis of the equations that describe what happens when shockwaves cross. "

What is surprising is that something as mild as interacting waves could create something as extreme as a space-time singularity, Temple said But it has been known since the 1960s that the jump in curvature created by a single shock wave is not enough to rule out the locally flat nature of space-time. A shockwave creates an abrupt change, or discontinuity, in the pressure and density of a fluid, and this creates a jump in the curvature. He found this created a new type of singularity, which he dubbed a "regularity singularity.

Temple and his colleagues are investigating whether the steep gradients in the space-time fabric at a regularity singularity could create any effects that are measurable in the real world. For example, they wonder whether they might produce gravity waves, Temple said. General relativity predicts that these are produced, for example, by the collision of massive objects like black holes, but they have not yet been observed in nature. Regularity singularities could also be formed within stars as shockwaves pass within them, the researchers theorize.

Reintjes, now a postdoctoral scholar at the University of Regensburg, Germany presented the work at the International Congress on Hyperbolic Problems in Padua, in June.