[lordfrito]

So with all this background churning, is it possible to periodically get the waves to line up and interfere constructively to create "rogue waves" in spacetime? [1]

I might be huge comparatively but still too small to measure it's effects maybe?

[1] https://en.wikipedia.org/wiki/Rogue_wave

[raattgift]

That's an unexpectedly neat question.

Gravitational radiation can form caustics, so in one way, yes. This was an area of theory that Bondi and Pirani were interested in during the 60s to 80s. Caustics are meant in the sense of the bright spots in https://en.wikipedia.org/wiki/Caustic_(optics) but rather than some "rogue wave" you might get a black hole.

More recently mathematical-relativity studies of the stability of Kerr black holes included a 900+ page paper https://arxiv.org/abs/2205.14808 which among other things considers something like a rogue wave passing through a spinning black hole, and asking: does the black hole swallow up some of the wave? or does part of the wave get entrained into a sort of accretion disc? in that disc do caustics appear, and if so do they lead to black holes? if so, do those black holes fall in, fly away, or coalesce into long-term orbiting bodies around the original black hole? These questions were asked because "stability" means "if perturbed (e.g. by a powerful gravitational wave), does an initially Kerr-like black hole relax back into a Kerr-like black hole, or does it become something very much not like Kerr?".

Caustics may also form by a powerful gravitational wave gravitationally-lensing around some massive object like a heavy galaxy cluster. And if that massive object has enough angular momentum, it's possible the caustic will evolve into a significant gravitational wave enhanced somewhat analogously to a slingshot manoeuvre by a spacecraft.

Conversely, we can start with a rogue wave existing, and see what it does.

Bondi and Pirani were also interested in spacetimes with enormous gravitational wave impulses. One family of those is the "sandwich wave", https://royalsocietypublishing.org/doi/10.1098/rspa.1959.012... (1959) (put "https://sci-hub.se/ in front of that URL if you need to).

Loosely, it's called "sandwich" because the spacetime is pretty bland (like white bread?) or even flat on either side of the wave, which divides the spacetime into three parts (including the wave itself).

Thirty years later they showed that the sandwiches are pretty unhealthy as they tend to destroy everything in the universe they pass through (any set of finitely-but-widely-separated galaxy clusters in such a spacetime will end up colliding with each other in finite time). https://royalsocietypublishing.org/doi/10.1098/rspa.1989.001... (also on sci-hub, and with nice late-1980s diagrams).

Fortunately, I don't think anyone has any idea how to generate a sandwich wave - it's just a feature of the spacetime put in by hand.

Unfortunately, we could be in a sandwich spacetime and not know it yet. A sci-fi writer might speculate about a preferred orbital plane for a large number of (very-early-universe-born) supermassive black hole binaries building up an approximate sandwich wave over the course of billions of years. Or perhaps speculate that the apparent stochastic background that's the topic of the fine link at the top where I guess you get "churning" from is not caused principally by supermassive black hole binaries but by some tensor-mode reheating during cosmic inflation (or a false-vacuum-to-real-vacuum first-order (not as in recent Star Wars, or is it?) phase change), and that this effect happened to generate a sandwich wave which has already destroyed galaxies far far away. A hard-working hard science fiction writer might even be able to force a cosmologist to concede that such a picture might be consistent with observation, including the pulsar timing array results in today's news.

A sandwich wave would zip through our galaxy at the speed of light, but the sandwich-wave-induced collapse of the galaxy into a caustic might take enough time that you could really what's-the-opposite-of-enjoy the experience. Pleasant dreams.

[lordfrito]

Wow thanks for the insightful answer.... Never heard of caustics before, but that is a much better analogy I think. The fact this stuff can and does exist makes sense. Caustics caused by gravitational lensing is something I can naïvely visualize.

I'm struggling to understand how a sandwich wave causes "everything in an infinite spatial volume becomes known in a finite time". Armchair physicist here.

Crazy that this stuff has already been studied 40 to 60 years ago.

[raattgift]

> struggling to understand

> Armchair physicist here

I've started and aborted a couple of ELI-n where n < ~ 24, and I'm not sure this one is especially satisfying either, but I think my previous attempts were just confusing and went beyond your implied question.

Causality in a sandwich wave spacetime is weird. All the null geodesics from a point can eventually refocus on some future point in the afterzone. We can take that simple fact (from Penrose initially) and contrive a sandwich wave spacetime that shows off the Bondi&Pirani words that confused you.

If you do an isotropic pulse of light in the beforezone, as expected (beforezone being just the flat spacetime of special relativity) it flies outwards in an expanding spherical shell. In a flat spacetime without a sandwich wave, you'd never see any of it again in the absence of a reflection. However, in the sandwich spacetime the gravitational wave can roll over you (and this expanding shell of light) such that in the afterzone all the light that you flashed out isotropically, eventually lands all at once on your eyeball, no mirrors required.

Moreover, the null geodesics out of multiple different points can all be refocused on just one future point. So you can fire off dozens, millions of isotropic flashes in the beforezone, and fry your eyeball (in the future, in the afterzone) to a crissssp.

Going further, one can set up a sandwich spacetime so that the light from every event in the beforezone lands on one point in the afterzone, or on a succession of time-ordered points. In this way, an observer in the afterzone can in finite time receive light from every light-emission in the beforezone, even if the beforezone is infinite.

Finally, I am using "light" loosely; to keep the sandwich spacetime flat except for the wavezone, instead of light we need massless test particles that feel gravitation only passively. They don't exert an active influence on the gravitational wave or on the focal point in the afterzone, even if there is an awful lot of them. More technically, we need the stress-energy tensor to be 0 everywhere in the whole (vacuum) sandwich spacetime, otherwise we will have a lot of work[1] exploring the contrived spacetime's insensitivity to perturbations from matter (which generates curvature after all, and a heavy enough amount can distort the wavezone). Matter here includes light.

- --

[1] there is a literature in that area, with Mustafa Halilsoy being fairly prominent in studies of (matter) waves including standard electromagnetism interacting with the sandwich (gravitational) wave, which in turn invited thoughts about (non-sandwich) gravitational waves interacting with the sandwich wave, which is also in the literature. I'm not likely to ELI any of that here though.