Speed of Gravity in a medium

[Gerinski]

It is clear that gravity propagates at the speed of light in the vacuum. But what happens to gravitational waves as they propagate through material mediums? Presumably they get slowed down but, is it known precisely how much and by which factors, density of the medium or any other properties?

And what if the gravitational waves propagate through a region of space which is itself 'warped' by gravity (by say, a neutron star or whatever).

Or are they affected for example by heavy electromagnetic fields, in a similar (reciprocal) way as EM radiation is affected (bent) by gravity?

In summary, how good is our understanding of the propagation of gravity through mediums other than the perfect vacuum, and through other energy fields?

Thanks!

 

[haushofer]

Just a quickie: you need to take the weak-field approx. with a non-vanishing energy-momentum tensor of the medium. Could be an interesting exercise to do that for e.g. a simple fluid and see what kind of equation you end up with.

 

[Dale]

But what happens to gravitational waves as they propagate through material mediums?

Really great question.

I don't know the answer, but where I would start is by looking at the linearized equations and see if there is anything that would give an indication.

 

[PAllen]

The following discusses propagation of GW through matter in section five. The overall conclusion is that, in principle, there is a tiny affect on speed, but that it is insignificant in practice. For observational purposes, you can say intervening matter does not scatter, refract, nor diffract GW. However, a large mass can gravitationally lens GW, just as if it were light (this follows from the geometrical optics approximation being valid, as demonstrated in section four of this reference.)

https://www.lorentz.leidenuniv.nl/lorentzchair/thorne/Thorne1.pdf