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**Are the equations of relativity "closed"**

Are the equations of relativity "closed" i mean if we can add an extra term of 0 covariant derivative to them without alter thes olution i mean if we have the equations

Gab=Tab , will the equations

Gab+Uab=Tab with DUab=0 (covariant derivative)

can both equation provide the same geometrical interpretation of gravity?...

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