The speed of gravitational waves -which is the same as the speed of light- depends on the metric which in turn depends on the presence of matter/energy.  But the effect is very small for ordinary densities of matter.

Thanks.

Electromagnetic waves are not slowed down by matter - a proportion of the energy is absorbed and re-radiated (coherently) with a delay and phase change.  I imagine this happens with gravitational waves - the detectors must have absorbed some of the energy from the waves, likewise the earth will have absorbed some of the energy, and wobbled infinitesimally and given off a small gravitational wave with a different phase.  In a very dense field of planets this might have a noticeable effect on gravity waves, resulting effectively in a time delay.  

To say that electromagnetic waves are not slowed down when they propagate through matter really depends upon the model you are using - and they are all just models.

The absorption, re-emmission model explains what is happening at an atomic level but as the wavelength is much greater (for light and electrical waves) than the interatomic spacing one has to treat the process over many atoms and a continuous model is perhaps more appropriate. In this case one sees the speed of light reduced from that in vacuum. This model helps explain a wide variety of phenomena and is the basis for the derivation of Snell's law. If you make the measurement you'll find that if you put light into a medium it comes out later than one would calculate from a vacuum and so arguing that the light is slowed down is not unreasonable. Indeed people have brought it to a stop and in this case it is clearly absorbed.

Anyway my question was not so much about the detail but more about wether the same type of phenomenon is predicted for gravitational waves.

The important point is that the speed of light-or gravitational waves-travelling at a point in vacuum is affected by metric tensor at that point.  And the metric tensor or gravitational field is determined by the presence of matter at other points.  We know that gravitational fields bend light; they also slow it down. The slowing down of light travelling through a material medium is another unrelated phenomenon described by the interaction of light with the medium (its electrons, atoms, and molecules).  We should not confuse these two phenomena.

Since the light has a gravitational wave component, the gravitatonal wave would slow down as the light does.

C.Y. Lo.  I'm not sure that's relevant. Particles have a gravitational component and travel slowly. I was talking of gravitational waves that have left the source.

I recommend readers of the discussion see P. C. Peters's paper:

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