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Something moving in our reference frame has a mass increase from the kinetic energy it has in our reference frame. It just doesn't turn into a black hole. I don't yet intuitively understand why (without doing the work of calculating it which might be a lot of work), but:
Lorentz covariance is a property of our current theories of physics, so a calculation according to our current theories must return that result (that whether an object is a black hole or not is independent of speed).
So, it does no good to sarcastically say that that our current theories must return some other result, and then try to use that claim of what you think the calculation would return as evidence against current theories.
I don't understand you.
Are those galaxies relativistically "deformed" or not?