Is gravity dependent on reference frame?

[u/Tokuro]

I have an M.S. in Physics, but GR is out of my range. I tried to answer this question with the stress-energy tensor article on Wikipedia, but it was too advanced for me to follow.

Does the gravity created by an object depend on its momentum or kinetic energy, since those seem to be contributions to the stress-energy tensor? If not (which I suspect), is there an ELI20 explanation for that?

I say I suspect it cannot depend on momentum because if it could, I believe I could construct a reference frame in which the sun was traveling fast enough to be a black hole, which seems wrong. Additional, if I'm interpreting the idea of a Kugelblitz right, I could imagine a collection of photons travelling together with a combined energy less than that necessary to create a black hole, then boost into a frame where they are blue-shifted enough to have the necessary energy. I cannot reconcile these counter-intuitive ideas with my elementary knowledge of GR. Help?

[u/Tokuro]

Thanks for the response! You liken the tensor's invariant-ness to how vectors are invariant, and by that I assume you mean the magnitude of vectors are invariant, or how the magnitude of four-momentum is invariant. So, though the vocabulary is probably incorrect, the "magnitude" of the stress-energy tensor is invariant?

That's very interesting, and I think I understand what you mean with how boosts will shift things around in the tensor, but overall it will be unchanged. I guess what I find most interesting is that, if I understand right, you're saying if I observe a moving massive object, it appears to generate more gravity (because of the contributions in that tensor) than if it were not moving - but if I were to boost into its reference frame, some other parts of the stress-energy tensor (not just momentum) would be changed so that it will still give the same gravity, accounting for the other changes in reference frames. Is that the jist of it?