Kostik's latest activity
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Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.The energy momentum tensor in contravariant form is constructed in a straightforward way for a dust, perfect fluid, etc. See for... -
Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.The conservation law ##{M^{\mu\nu}}_{,\nu} = 0## requires that ##\nu## be in a contravariant position.
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Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.The Dirac-Einstein pseudotensor is definitely not symmetric (with the indices in any position). So this seems a good reason to prefer...
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Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.I meant the Landau-Lifshitz pseudotensor is symmetric, while the Dirac-Einstein pseudotensor is not. I wasn't referring to the...
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Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.Yes, I am thinking of the contravariant ##T^{\mu 0}## as the energy and momentum. If you lower one of the indices with the metric, you...
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Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.@PeterDonis I'm still struggling with this. Perhaps I should have phrased the question a more direct way: (1) If...
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Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.@PeterDonis That's probably a little over my head. Yes, I agree it makes sense to deal with ##({t_\mu}^0 + T_\mu^0)\sqrt{-g}\,## prior...
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Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.@PeterDonis I would appreciate your comments if any on how to deal with the index positions, to get a contravariant quantity which can...
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Kostik reacted to PeterDonis's post in the thread A Dirac's integral for the energy-momentum of the gravitational field with
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That's certainly true of Dirac, not just here but in general. And reading the text following (31.4), his assumptions (a) and (b) do... -
Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.It is implied in the sentence I quoted. I did the work in my post above. Dirac doesn't fill in every step. Please just kindly read the...
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Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.You integrate both sides of (31.2).
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Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.You are confusing the 3D integral of the pseudo tensor with ##\nu = 0## with the 4D integral of (31.2).
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Kostik replied to the thread A Dirac's integral for the energy-momentum of the gravitational field.I think it's pretty clear from his comment "The equation (31.2) then shows that the integral (31.4) taken at one time ##x^0=a## equals...
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Kostik posted the thread A Dirac's integral for the energy-momentum of the gravitational field in Special and General Relativity.See Dirac's brief treatment of the energy-momentum pseudo-tensor in the attached picture. Dirac is presumably integrating eq. (31.2)...
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Kostik replied to the thread A A global energy conservation law in general relativity.@PeterDonis What special coordinates is Dirac using? I don’t see that.
