# warp drive with gravitational waves in the nonlinear regime

gravitational waves are strictly transversal (in the linear regime at least), also their amplitudes are tiny even for cosmic scale events like supernovas or binary black holes (at least far away, maybe we should ask some physicists located a bit closer to the center of the galaxy), but lets put all those facts aside for a second and consider a gravitational source big enough to generate gravitational waves with amplitudes of the order of the galaxy. For instance consider a planar wave like in my mediocre drawing:

$$h_{\alpha \beta} e^{i (k_{y} y - \omega t)}$$

where

$$h_{\alpha \beta} \approx 1$$

so the perturbation is in the nonlinear regime

i draw two far away objects in three different time slices (this is why they are repeated 3 times), the topmost is the objects without the gravitational wave, the one in the middle represents the objects in the crest of the gravitational wave, and the one in the bottom represents the objects in the valley of the wave.

So, my point is that people would only have to travel an arbitrarily small distance when the wave is on the valley (assuming circular polarization) even if the "normal" distance (i.e: $h_{\mu \nu} = 0$) is several light-years away

Besides being slightly impractical to set up such a mammoth gravitational source, this kind of warp drive is valid from a physical standpoint? Are there any physical limits to gravitational wave amplitudes in such nonlinear regime?

-
@lursher I'm guessing a gravitational field strong enough to shrink a distance by a significant proportion of its beginning value would be stupendously nonlinear: much stronger than describable by weak field Einstein equations. I'm very rusty on GR: I'm guessing that there are nonlinear wave solutions or approximations or known wave behaviours from numerical simulations - and that you are invoking these nonlinear behaviours is this right? –  WetSavannaAnimal aka Rod Vance Aug 21 '13 at 1:46
And how would the would be spacefarer feel in such a strong wave? Could the metric be such that the locally flat regions were big enough to include all of the points in his-her body - so that spaghettifying stresses were not set up? –  WetSavannaAnimal aka Rod Vance Aug 21 '13 at 1:50
@WetSavannaAnimalakaRodVance: FWIW: you have the plane wave spacetime, which is an exact solution to the vacuum einstein equation: arxiv.org/abs/1203.6173 –  Jerry Schirmer Sep 19 '13 at 23:28
And if you read the linked arxiv article, the authors report a closed null curve in a particualr class of plane wave spacetime. So I'm inclined to say that the answer to lurscher's quesiton is "probably yes", but then you start have to ask questions about generating sufficiently large gravitational waves with the correct waveform using matter satisfying the usual cosmic censorship-style assumptions. –  Jerry Schirmer Sep 19 '13 at 23:30
@JerrySchirmer Hilarious! I am having a great deal of fun reading Roald Dahl with my children at the moment, and I'm sure if he were alive he would have fun with such a gruesome thought! –  WetSavannaAnimal aka Rod Vance Sep 20 '13 at 1:33

I don't think you could use this as a warp drive unless you could collimate the gravity waves. If you consider a spaceship moving at constant velocity through a gravity wave, the ship will be accelerated then decelerated again as the wave passed through but it's average velocity would be unchanged. The only way you could get a net effect from the wave is if you could move from a region of high amplitude to low amplitude within half a cycle of the wave. I can't think of any (plausible) geometry that would allow this. Possibly you could do it very close to a black hole binary, where the gravity wave generation doesn't look like a point source.

-
the gravity wave does not produce any "acceleration" in test particles in the traditional sense of changing net momentum, it is just an oscillation in the metric, so the distance between the far-away objects grows and shrink in a single period by an amount proportional to the wave amplitude. So all objects at every point in the gravitational oscillation are always in free fall. –  lurscher Jun 22 '12 at 13:06
regarding physical plausibility, i agree, it is usually hard to come by with sources of planar waves, and the fact that its gravitational radiation we are talking about does not make it any more realistic. –  lurscher Jun 22 '12 at 13:20