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martinbn

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So the question is how does one make the statements precise?

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martinbn

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So the question is how does one make the statements precise?

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PeterDonis

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martinbn

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PeterDonis

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The surface area is better than the vague ##R##, but it still depends on the space-like slice.

Technically, yes, but for an asymptotically flat (i.e., isolated) system, one can define what amounts to a center of mass frame and use that to define the spacelike slices. Until we get a proper theory of quantum gravity, that's probably the best we're going to be able to do, since without one we simply don't know the precise microscopic degrees of freedom of a system including the spacetime geometry.

how is the mass defined?

The ADM mass or the Bondi mass would be the simplest definitions, since they apply to any asymptotically flat system. I would lean towards the latter since it takes into account radiation emitted out to infinity.

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I think this could be the answer:So the question is how does one make the statements precise?

https://arxiv.org/abs/hep-th/9905177

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