In general relativity, the speed of gravitational waves was a matter of Einstein's arbitrary choice. He tweaked the coordinates so that gravitational waves could travel at the speed of light, and Arthur Eddington was surprisingly honest in exposing this
particular hoax:
Arthur Eddington: "If coordinates are chosen so as to satisfy a certain condition which has no very clear geometrical importance, the speed is that of light; if the coordinates are slightly different the speed is altogether different from that of light.
The result stands or falls by the choice of coordinates and, so far as can be judged, the coordinates here used were purposely introduced in order to obtain the simplification which results from representing the propagation as occurring with the speed of
light. The argument thus follows a vicious circle." The Mathematical Theory of Relativity, pp. 130-131
https://www.amazon.com/Mathematical-Theory-Relativity-S-Eddington/dp/0521091659
Arthur Eddington: "The problem of the propagation of disturbances of the gravitational field was investigated by Einstein in 1916, and again in 1918. It has usually been inferred from his discussion that a change in the distribution of matter produces
gravitational effects which are propagated with the speed of light; but I think that Einstein really left the question of the speed of propagation rather indefinite. His analysis shows how the co-ordinates must be chosen if it is desired to represent the
gravitational potentials as propagated with the speed of light; but there is nothing to indicate that the speed of light appears in the problem, except as the result of this arbitrary choice."
http://rspa.royalsocietypublishing.org/content/royprsa/102/
716/268.full.pdf
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