Did General Relativity predict any mass changes of objects in a strong gravitational field?
Not sure what you are getting at....GR doesn't work so well in the most extreme gravity...black holes....
gravitational forces within a black hole will tear any entering matter to shreds...apparently space ends and is replaced by only time....I assume mass as we know it disappears...in any case mass defect (binding energy) must be recouped as nuclear constituents are ripped apart....do only fundamental constituents then remain?? What about string constituents??
Mass will also undergo curved motion, acceleration and if greater velocity increased kinteic energy and relativistic mass when moving freely in a gravitational field.
Mass is the norm of the four-momentum, so I believe that it is invariant regardless of the curvature tensor.
For an extended test mass, the norm of the four-momentum actually can change. Part of this may be interpreted as being due to shifts in the gravitational potential energy (which act something like inertia). The rest arises from an effect somewhat analogous to electromagnetic induction.
Are you saying all motion stops?
I don't know. I doubt anybody does and perhaps many would disagree with the boldface in your/my post.
My post that "apparently space ends and is replaced by time" comes from one of the popular physicsts (maybe Brian Greene or Lee Smolin, I can't find the reference now.) Not knowing all the assumptions nor the math at black hole extremes where relativity and QM breaks down, your guess is as good as mine.
I would rather guess that at such extremes much of what we know as "normal" space,time,mass,time,motion, energy,etc likely changes in extreme ways and is likely unrecognizable in terms of everyday experience. If one or more of those is fundamental and others emergent, then I would also guess the emergent factors disappear first, maybe leaving fundamental constituents....perhaps those become "altered" as well....
My own guess (not a belief) is that all such consituents are linked in ways we barely understand....a simple example relationship is E=mc^2 which rocked the world when Einstein made it known.
the original question
makes me wonder that since gravitational fields are self interacting ( unlike electromagnetic fields), when a mass (maybe a planet, maybe a distribution of particles) is in place with it's own gravitational field and a gravitational wave passes, not only does the mass accelerate/pulse transverse to the direction of wave propagation but the gravitational fields also interact....so now the original mass is not only vibrating but it's magnetic field is altered and it is also radiating a gravitational field...lots going on!!!
It's hard for me to imagine the original mass isn't altered in some subtle/extremely small way.
There is an excellent pictorial of the effect of a passing gravitational wave at :
I find it interesting that some physicists think motion stops but then others think black holes have entropy and a tempeture. My understanding of tempreture is that it is a measure of the molecular motion. So if motion stops then a black hole can't have a tempeture. No matter how you look at it something isn't correct. Either out definition of tempeture needs to be refined. Hawking or those physicists are incorrect or i'm missing something(most likely the last option)
That is where the problem lies. The definition of temperature relies on the number of microstates per energy. This can be related to molecular motion (as with more total energy, there are more states the particles can be in and they will have a greater average velocity), but it is not necessary for there to be motion.
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