Is it an assumption that the speed of propagation of gravitational waves is exactly the same as the speed of light? If the speed of gravity is only slightly less than the speed of light, the effect might not show up over solar or intra galactic distances, but over extragalactic distances could it give the appearance that there is dark matter influencing motion?
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$\begingroup$ @Hohmannfan Indeed, his answer is over there $\endgroup$– Sir CumferenceSep 16, 2016 at 2:13
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2 Answers
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It has long been one possibility that gravity does not work as in general relativity, or as in the Newtonian limit that is relevant to the gravity in a galaxy. Thus, many different modifications to gravity have been tried. But the reason they are generally not very successful is that dark matter seems to alter gravity on many different scales, from within a galaxy, to over galaxy clusters, to the expansion of the universe as a whole. Thus it generally requires multiple different modifications to fit them all, and that makes for a very clunky model of gravity-- one can fit anything if given enough free parameters. That sounds like it would be the problem for trying something based on the speed of gravity-- the timescale for propagation of changes would be very different over the three scales I just mentioned, yet dark matter has a similar influence on all three scales.
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The fact that gravitational waves propagate at the speed of light is not an assumption, but is derived from the assumption that nothing travels faster than light. In General Relativity, you build a metric, which is a tool to be able to measure and locate events in space and time. Building this metric puts constrains on the speed of information, and a basic assumption is that this speed is at most $c$ and is equal to $c$ if the information carrier is mass-less (photons for example).
Gravity waves are small non-static perturbation of this metric in the void. So they are propagating information without any mass and travel at $c$.
Of course, this is a physical approach to your question, answering it correctly would involve much harder calculations to perturb the metric, obtain the propagation equation and study the speed of the waves. This is for example explained in the wikipedia article in the linear section.
I can think about an example (correct me if I'm wrong). Think about a massive object collapsing into a black hole. This is an extremely energetic process, if light was able to get out of the forming black hole, you would see it shining like a extremely bright supernova. To my knowledge there is no evidence of that.
More theoretically, I think that the assumption that light travels faster than gravity is incompatible with the cosmic censorship hypothesis,
