sqljunkey said:
People in this thread have been saying that as soon as you have curvature in the spacetime you will see these test masses start free falling along these geodesics.
Test masses will free fall along geodesics whether spacetime is flat or curved. Curvature just changes the relationship between different geodesics.
sqljunkey said:
Gravitational waves, are curves in spacetime. So I would assume that as soon as these waves hit test masses they will start free falling alongside those geodesics.
They won't "start" free falling--they'll be free falling the whole time. But as a result of the gravitational wave passing, the relationship between the different geodesics that nearby test masses are free-falling on will change. That is exactly what a gravitational wave detector like LIGO is detecting: the change in the relative motion of different test masses due to a gravitational wave passing.
sqljunkey said:
I extrapolated that since these waves move along one spacetime they will probably interact with one another.
Since the Einstein Field Equation is nonlinear, yes, in principle gravitational waves can interact with one another. In practice, any gravitational waves we can detect here on Earth are so weak that the nonlinearities are negligible, and they can be treated like linear waves, which just superpose without any interaction between them--as, for example, EM waves do.
sqljunkey said:
there could be a hypothetical situation where these waves in spacetime cancel each other out and create a total flat space
You should first ask yourself if this is possible with EM waves: can EM waves cancel each other out and create a region where there are zero EM fields whatsoever? And if so, how large can such a region be?
(Hint: the answer is that while EM waves can cancel each other out at particular points, they can't cancel each other out completely over an extended region.)
sqljunkey said:
This could all be happening near a massive star.
Near a massive star, even at points where incoming gravitational waves do cancel each other out, that doesn't remove the static spacetime curvature due to the star. You can't cancel out that kind of spacetime curvature with gravitational waves at all.
sqljunkey said:
In my opinion when they came with the idea of gravitational waves they were saying that GR was in fact the theory of gravity.
This is nonsense. GR was known to be a theory of gravity as soon as it was invented, and this had nothing to do with its prediction of gravitational waves. It had to do with all the predictions it made that matched Newtonian gravity, plus the additional predictions it made that accounted for phenomena that couldn't be explained by Newtonian gravity (like the precession of Mercury's perihelion), and also predicted new phenomena that had never been observed (like bending of light by the Sun and gravitational redshift).
sqljunkey said:
It didn't matter anymore if there was no mass or no energy in the south, you can still be compelled to free fall in that direction.
I have no idea what you mean by this.
