Gravitational waves speed in a medium

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Gravitational waves are predicted to travel at the speed of light in a vacuum, similar to electromagnetic waves, but their behavior in material mediums remains uncertain. Current calculations typically assume negligible mass-energy outside the source region, making it challenging to determine how gravitational waves would be affected by a medium. Research by Ingraham suggests that the speed of gravitational waves could be less than c when propagating through large molecular gas clouds, though the effect would be minimal. Recent findings from aLIGO have established a strict upper limit on dispersion, indicating that any potential slowing of gravitational waves in a medium is likely negligible. Understanding this phenomenon remains an area for further exploration in gravitational wave physics.
Gerinski
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Electromagnetic waves are known to travel a c in a vacuum, but at lower speeds in a material medium.
What about gravitational waves? They are also predicted to travel at c in a vacuum, but what about them traveling through material mediums? Do they get slowed down? by which factor?

TX
 
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I doubt there has been much work done on that. The calculations I have seen regarding gravitational waves have all assumed that outside the source region there is negligible mass-energy, and accordingly assumes the stress-energy tensor outside the source to be zero. Since a medium has mass, the question of speed through a medium would be outside the scope of such calculations.
 
See Ingraham, "Gravitational waves in matter," GRG 29 (1997) 117. Ingraham suggests that the best chance for seeing ##v<c## might be in "gravitational wave propagation through molecular gas clouds of galactic or intergalactic size." Although n−1 would be incredibly small, he suggests that you might be able to see an effect accumulated over thousands or millions of light-years.

Note that the recent aLIGO result puts a very tight upper limit on dispersion.
 
In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...

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