SR and GR in a medium, gravitational waves

[haushofer]

A little question which I thought of today.

I thought about what happened in a medium with Lorentz transformation. With a refraction index n, the speed of light is altered to c/n. However, as far as I can see now this shouldn't influence the Lorentztransformations, right? It's tempting to put c --> c/n in the Lorentz transformations. If this would be the case, one would have a hard time explaining things like Cerenkov radiation. Also, photons interact with the electromagnetic properties of a material, but we could think of massless particles without charge. So it seems that the idea of putting c to c/n in a Lorentz transformation would "single out" photons, while the axiom "all inertial observers measure the same speed of light" shouldn't depend on the particular massless particle you could take. Could some one comment on that?

But what about gravitational waves in a medium? I don't see how the linearized Einstein equations with non vanishing energy momentum tensor would still give a wave equation with a speed exactly equal to c. And what would be the vacuum around which we do this linearised expansion? How would we perform such a perturbation, and are there articles or books about this?

And also something which has bothered me a long time about gravitational waves: what about the case in which we can't perform a linearisation? Is it true that for arbitrary "massive/energetic" sources we still have gravitational waves which travel at c? At some point our perturbation breaks down, I would say, and then we would have a hard time getting a wave equation.

Just some thoughts :)

 

[Dale]

With a refraction index n, the speed of light is altered to c/n. However, as far as I can see now this shouldn't influence the Lorentztransformations, right?

You are correct. The invariant speed, c, is the speed of light in vacuum, not in the local medium.

 

[atyy]

In a medium, the refractive index usually is a function of frequency, so the speed of light will be a function of frequency, and there should not be Lorentz invariance, except in special cases.

Yes, the gravitational wave picture breaks down if a linearization cannot be performed.

 

[atyy]

There is a discussion of the effective mass of the photon in Cerenkov radiation on p130 of http://books.google.com/books?id=Lh0tjaBNzg0C&dq=cerenkov+AND+photon+mass&source=gbs_navlinks_s

 

[haushofer]

Yes, the gravitational wave picture breaks down if a linearization cannot be performed.

So what are the reasons to believe we still have gravitational waves beyond that point?

 

[atyy]

So what are the reasons to believe we still have gravitational waves beyond that point?

You can write the Einstein Equation as a nonlinear wave if the spacetime can be covered by harmonic coordinates. But I don't know if the "waves" there mean the same thing as gravitational waves as small perturbations on a background spacetime.