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1)Changing of body velocity or reference frame don't contribute to spacetime curvature

2)On the contrary the change of body mass causes the change of curvature in local spacetime

I use the assumption that if we have the same tensor in the right part of Einstein field equation the curvature remains the same and changes othwerwise

$$R_{\mu \nu} - {1 \over 2}g_{\mu \nu}\,R + g_{\mu \nu} \Lambda =

{8 \pi G \over c^4} T_{\mu \nu}$$

My suggestion is:

1) Let a body with some velocity has stress-energy tensor ##T##. Then in another reference frame let the body stress-energy tensor be ##T'##. As stress-energy tensor is invariant we should get the same tensor but different coordiantes when changing velocity or reference frame . Will it be the proof if I manage to find ##\Lambda## from the following equation and show that it is a linear transformation

$$T_{\mu' \nu'}'={\Lambda^{\mu}}_{\mu'} {\Lambda^{\nu}}_{\nu'} T_{\mu \nu}.$$

2) Let a body be stationary and has some mass. Its stress-energy tensor is ##T##. Then we change the mass of a body and get ##T'## for its stress-energy tensor. So we should have ##T \neq T'##. Can I use the previous equation here to prove this?

Can this work? Or I need to use the Riemann tensor and Richi scalar in the left part Einstein field equation?

Thank you.