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does anybody know a proof of the equivalence (or differences) between the "total mass" integral \int T_munu \xi^mu dV^nu and the "Komar mass" integral \int R_munu \xi^mu dV^nu ?

(here \xi is the timelike killing vector, dV is a 3-volume, and spacetime is assumed asymptotically flat, in addition to stationary)

Recall that both these integrals are constant of motion, and for Schwarzschild they are both equal to "m"....

The only reference to this proof I know, is exercise n.4 in cap.11 of Wald, but that assumes weak field... Then a paper by ashtekar (JMath Phys 1979) also proves the equality of the ADM and Komar integrals.. but still the total mass is not mentioned.

Does anybody have some insight or a good reference to this point?

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# Total energy/mass in stationary GR

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