### A wrinkle in space-time

##### July 20, 2012

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.”

**Background**

Einstein’s theory of general relativity explains gravity as a curvature in space-time. But the theory starts from the assumption that any local patch of space-time looks flat, Temple said.

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.

**How shockwaves can affect the curvature of space-time**

Temple and his collaborators study the mathematics of how shockwaves in a perfect fluid can affect the curvature of space-time in general relativity. In earlier work, Temple and collaborator Joel Smoller, the 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.

A shockwave creates an abrupt change, or discontinuity, in the pressure and density of a fluid, and this creates a jump in the curvature. 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.

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. He found this created a new type of singularity, which he dubbed a “regularity singularity.”

What is surprising is that something as mild as interacting waves could create something as extreme as a space-time singularity, Temple said.

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.

### References:

- Moritz Reintjes, Blake Temple, Points of general relativistic shock wave interaction are ‘regularity singularities’ where space–time is not locally flat,
*Proceedings of the Royal Society A*, 2012, DOI: 10.1098/rspa.2011.0360 - Zeke Vogler, Blake Temple, Simulation of general relativistic shock wave interactions by a locally inertial Godunov method featuring dynamical time dilation,
*Proceedings of the Royal Society A*, 2012, DOI: 10.1098/rspa.2011.0355

## comments 9

September 18, 2012by Skylight

That might be assuming that gravity waves behave like water waves. Occasionally they amplify each other creating monster waves. But if on the other hand they behave more like light waves I would expect them to pass through each other uninterrupted. Just spit balling here.

August 2, 2012by Graham Rounce

It would have been better if the article had included some comments from other workers in the same field.

July 22, 2012by egore

Constant collisions should cause an interreaction .

July 21, 2012by egore

Holey Wormhole, Batman! I bet the Hadron Colider does the same thing on a smaller scale!

July 20, 2012by Chris

So sometime in the future, two black holes collide causing a wrinkle in the fabric of time and space causing some poor schmo to be cast back in time a few thousand years. Said schmo has a body full of respirocytes, winds up in the middle east and decides to go around healing people and espouse stories of a future filled with eternal life and stuff… Sure would explain a lot…

July 20, 2012by Gorden Russell

Great jokes, guys. I just wish the article had said more about what they think we’d see in this regularity singularity — outside of the gravity waves, that is. Of course, observing gravity waves would be a big deal in itself.

July 20, 2012by Bri

Sorry you’ll, I just can’t resist……… If your having trouble with wrinkles in space,,,,,, try some Botox. Brings new meaning to “fold,spindle,and mutilate”. More than enough to suggest space can be manipulated. Get your warp drive engines out!

July 20, 2012by GatorALLin

..if I could just get this black hole to collide with this supernova…then I could go back in time…..for about 10 minutes… now it takes a hundred light years to get there….oh never-mind…

July 20, 2012by GatorALLin

..if I could just get this black hole to collide with this supernova…then I could go back in time…..for about 10 sec… now how do we get over there?