There’s a hole in my spacetime! Or a string, or a wall…

“The whole fabric of the space-time continuum is not merely curved, it is in fact totally bent.” –Douglas Adams

As many of you know, if you take a whole bunch of mass, and you’ve got nothing going on except gravity, it’s going to gravitationally collapse. And if atoms, nuclei, pressure, and nuclear reactions don’t (or can’t) prevent that gravitational collapse from running away, you’re going to wind up with a black hole.

But last week, I told you that if you took all the matter in the Universe and shaped it into a cylinder, you’d actually wind up with a huge cylinder of solid matter, as big around as the Earth’s orbit around the Sun!

But this cylinder, unlike the other shapes, wouldn’t collapse down to a black hole. A black hole would give you, literally, a point-like hole in spacetime (assuming that there aren’t violations of, for instance, the strong energy condition, which could happen in theory).

The fact that we observe evidence for black holes in many different regions, most prominently at the center of every large galaxy (including our own), tells us that we’re on the right track as to what’s going on.

But what if, instead of a hole, you had a huge string? What if, instead of a bunch of point-like (zero-dimensional) holes in your spacetime,

you had a network of string-like (one-dimensional) defects throughout spacetime?

While this might remind some of you of the Nexus from Star Trek: Generations, this is a real possibility in theoretical physics! (Although it hasn’t been observed.)

We learn something interesting about the expansion of the Universe from playing around with this idea of a cosmic string, or network of strings. (The wikipedia page is so bad I refuse to link to it.) First off, if we fill spacetime with 0-dimensional defects (point-like masses), the expanding Universe slows down its expansion, as gravity works to counteract the expansion. A model Universe, full of point-like black holes, can eventually have the expansion rate asymptote to zero, decelerating but never turning around. (Following the curve labeled B, below.)

Yet if that same Universe is full of cosmic strings (1-D defects), the expansion rate doesn’t decelerate! It follows curve C above, and a Universe filled with cosmic strings will continue to expand, with the expansion neither accelerating nor decelerating.

But you may decide to make things a little more interesting. What if, instead of 0-D or 1-D defects, you filled the Universe with domain walls, a 2-D topological defect? (Instead of a point or a string, a “sheet-like” defect in spacetime.)

Of course, this is observationally ruled out, too, but just for the fun of it, you get a Universe whose expansion rate accelerates! Mind you, it doesn’t accelerate the same way our observed Universe does; it doesn’t quite do it as quickly.

But if you change the dimension of your defects in spacetime, you can ad-hoc your way to any expansion rate you want.

And interestingly enough, if you decide to tweak your toy model of defects in spacetime to reproduce dark energy — the observed accelerated expansion of the Universe — what do you suppose you get?

Three-dimensional defects, known technically as textures! In other words, if you filled the Universe with the right amount of 3-D defects in spacetime, the expansion rate you’d see would match up perfectly well with the observed dark energy!

Before you get too excited, let’s be realistic, here. We’ve never detected any of these topological defects in 1, 2, or higher dimensions, so they’re only theoretical constructs. In principle, however, we know how we could make or generate them, and it’s pretty straightforward! (“Knots” in spacetime, theoretically caused by many things, spread out widely enough over 1, 2, or more dimensions.)

Searches for evidence of strings, domain walls, textures, and other defects are still ongoing, and although they’ve come up empty so far, detection of say, a texture, could revolutionize the way we think about dark energy! Some food for some deep (speculative) thoughts on a Monday; enjoy!