Gravitational energy as the product of a field by a moment

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Hello!
I was wondering if it is possible to express the gravitational energy as a product of the gravitational field by a moment, as we do with the magnetic and electric energy? Would this require the existence of bodies with negative mass? How could we relate this to the existence or total energy of a gravitational wave?
 
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Ibix
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The source term for gravitational radiation is a time varying quadropole moment, if that's what you mean. There's no dipole term possible because mass is always positive.

As far as I'm aware the only time an energy of the gravitational field is completely well defined is in the stationary case, which is just the gravitational potential. But by definition a changing quadropole moment is not stationary, so I don't think this applies.
 
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PeterDonis
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Moderator's note: Moved thread to relativity forum.
 
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Vanadium 50
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I was wondering if it is possible to express the gravitational energy as a product of the gravitational field by a moment
You mean can we take U = mgh and arrange it like so: U = g(mh)? Sure. But why?
 
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pervect
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Hello!
I was wondering if it is possible to express the gravitational energy as a product of the gravitational field by a moment, as we do with the magnetic and electric energy? Would this require the existence of bodies with negative mass? How could we relate this to the existence or total energy of a gravitational wave?
We've got about three different restricted definitions of energy in GR that I'm aware of, which in general are derived from the metric, and not from a 'gravitational field', which is a bit vague. These are due to Bondi, ADM, and Komarr, and none of them are in the form of mgh, which I am guessing what you mean by the product of a field (g) and a moment (mh). So I'd venture to say the answer is "no".

Most of the definitions we have of energy require asymptotic flatness, so they don't apply to an infinite expanding universe. Komarr's defintion is linked to Noether's theorem, which arose from Hilbert's investigations into energy in GR, and requires time translation symmetry. It also doesn't apply to an infinite expanding universe.
 
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