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

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Moving the Stress-Energy tensor (SET) to the left side of the Einstein Field Equations (EFE) does not change the underlying physics, as the mathematics remains consistent regardless of the placement. The discussion highlights that while some may argue about the relationship between dark energy and spacetime, the core principle is that the SET must equal zero to define a vacuum. The analogy of "two apples equals two apples" illustrates that rearranging terms does not alter the overall content of the equation. Ultimately, the position of the SET does not create a vacuum; it is defined solely by the tensor being zero. Thus, the placement of the SET in the EFE is a matter of preference rather than impact.
Fractal matter
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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?
 
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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.
 
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Fractal matter said:
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.
 

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