Why does it make sense that low-amplitude waves propagate at c? In Newtonian gravity, gravitational effects are assumed to propagate at infinite speed, so that for example the lunar tides correspond at any time to the position of the moon at the same instant. This clearly can’t be true in relativity, since simultaneity isn’t something that different observers even agree on. Not only should the “speed of gravity” be finite, but it seems implausible that that it would be greater than c; based on symmetry properties of spacetime, one can prove that there must be a maximum speed of cause and effect.[Ignatowsky, Pal] Although the argument is only applicable to special relativity, i.e., to a flat spacetime, it seems likely to apply to general relativity as well, at least for low-amplitude waves on a flat background. As early as 1913, before Einstein had even developed the full theory of general relativity, he had carried out calculations in the weak-field limit that showed that gravitational effects should propagate at c. This seems eminently reasonable, since (a) it is likely to be consistent with causality, and (b) G and c are the only constants with units that appear in the field equations, and the only velocity-scale that can be constructed from these two constants is c itself.
High-amplitude gravitational waves need *not* propagate at c. For example, GR predicts that a gravitational-wave pulse propagating on a background of curved spacetime develops a trailing edge that propagates at less than c.[MTW, p. 957] This effect is weak when the amplitude is small or the wavelength is short compared to the scale of the background curvature.
It is difficult to design empirical tests that specifically check propagation at c, independently of the other features of general relativity. The trouble is that although there are other theories of gravity (e.g., Brans-Dicke gravity) that are consistent with all the currently available experimental data, none of them predict that gravitational disturbances propagate at any other speed than c. Without a test theory that predicts a different speed, it becomes essentially impossible to interpret observations so as to extract the speed. In 2003, Fomalont published the results of an exquisitely sensitive test of general relativity using radar astronomy, and these results were consistent with general relativity. Fomalont’s co-author, the theorist Kopeikin, interpreted the results as verifying general relativity’s prediction of propagation of gravitational disturbances at c. Samuel and Will published refutations showing that Kopeikin’s interpretation was mistaken, and that what the experiment really verified was the speed of light, not the speed of gravity.
W.v.Ignatowsky, Phys. Zeits. 11 (1911) 972
Palash B. Pal, “Nothing but Relativity,” Eur.J.Phys.24:315-319,2003, http://arxiv.org/abs/physics/0302045v1
MTW – Misner, Thorne, and Wheeler, Gravitation
Fomalont and Kopeikin – http://arxiv.org/abs/astro-ph/0302294