I Move Stress-Energy tensor to the left side of EFE?

[Fractal matter]

Is it possible to move Stress-Energy tensor to the left side of EFE? R=T => R-T=0. Relativists move cosmological constant Λ to the right side of EFE. Can we move SE tensor to make a vacuum?

 

[Ibix]

You can move either tensor to either side. It makes no difference to anything. Because we don't know what dark energy/the cosmological constant is you can argue that it's a part of spacetime or it's a part of the contents of spacetime, and then it kind of makes sense to put it with the Einstein tensor or with the stress-energy tensor just in a birds-of-a-feather kind of way. The maths is the same, whichever side you put it.

You can take the stress-energy tensor to the same side as the Einstein tensor if you like. It doesn't make matter into a vacuum (unless it was already a Hoover).

"Two apples equals two apples" is equivalent to "two apples minus two apples is no apples". Neither statement makes any difference to the contents of my fruit bowl.

 

[PeterDonis]

Can we move SE tensor to make a vacuum?

No. "Vacuum" is defined as the SET being zero. Which side of the equation you put the SET on is irrelevant to that.