# How does gravitation propagate along curved spacetime?

In this wikipedia article it is described how a beam of light, with its locally constant speed, can travel "faster than light". That is to say it travels a distance, which, from a special relativistic point of view, is surprisingly big.

I wonder if a gravitational wave on such a curved spacetime (of which the wave is actually part of) behaves equally.

Does a gravitational wave also ride on expanding spacetime, just as light does? Do the nonlinearities of gravitation-gravitation interaction influence the propagation of a wave (like e.g. a plasma) such that light and gravity are effectively not equally fast?

If I want to send a fast signal in this expanding universe scenario, in what fashion do I decide to I send it?

• – Qmechanic Apr 21 '12 at 0:01
• I assume the real question you have is if there is any back-reaction. To be more specific, one might expect that in the limit of small gravitational waves on a static background, those waves would propagate with speed $c$. I can only say that in GR it does --- for details see any of the textbooks. I suppose from dimensional analysis one would expect nothing different as long as the wavelength was above Plank scale and below the radius of curvature of the underlying static background. – genneth Apr 21 '12 at 0:47
• @genneth: Yes, that's exactly my question. (I can't even see how the question can be read otherwise, the answers explain points regarding locally constant speed and faster than light even if that's both pointed out in the first line of my post. In the question section I emphasise the gravitation-gravitation interaction and give the plasma analog.) I don't see yet how you conclude from dimensional analysis to a pure linear propagation, though. – Nikolaj-K Apr 21 '12 at 10:18
• You don't get linear dispersion from dimensional analysis (at least I don't) --- you go to full GR and calculate the propagation of small ripples on a background --- this can be found in textbooks. The question of in what regimes this is a good approximation is/can be answered by dimensional analysis. – genneth Apr 21 '12 at 10:28
• +++ Just as a comment, I don't consider this question answered. – Nikolaj-K Aug 8 '12 at 18:22

Anyhow, the "faster than $c$" motion referred to in your link is similar in that it's a matter of geometry and the co-ordinates you're using. Since it's just geometry gravity waves will be affected in the same way as light, as indeed will everything that propagtes in space including objects with a non-zero rest mass.