Gravitational Energy: Field x Moment

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Discussion Overview

The discussion revolves around the possibility of expressing gravitational energy as a product of the gravitational field and a moment, similar to how magnetic and electric energy are expressed. Participants explore whether this formulation necessitates the existence of negative mass and its relation to gravitational waves.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants propose that gravitational energy could be expressed as a product of the gravitational field and a moment, questioning if this requires negative mass.
  • One participant notes that the source term for gravitational radiation is a time-varying quadrupole moment, emphasizing that a dipole term is not possible due to the positivity of mass.
  • Another participant mentions that the energy of the gravitational field is well-defined only in stationary cases, which contradicts the application to a changing quadrupole moment.
  • There is a suggestion that while one could rearrange the gravitational potential energy formula (U = mgh) to U = g(mh), the rationale behind this is questioned.
  • One participant highlights that there are multiple definitions of energy in General Relativity (GR) derived from the metric, specifically mentioning Bondi, ADM, and Komar definitions, which do not align with the proposed formulation.
  • Concerns are raised regarding the applicability of these energy definitions in the context of an infinite expanding universe.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of expressing gravitational energy in the proposed manner, with no consensus reached on the necessity of negative mass or the applicability of existing energy definitions in GR.

Contextual Notes

Participants note limitations regarding the definitions of energy in GR, particularly their dependence on asymptotic flatness and the implications for an infinite expanding universe.

jaumzaum
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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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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.
 
Moderator's note: Moved thread to relativity forum.
 
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jaumzaum said:
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?
 
jaumzaum said:
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 definition 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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