Kostik's latest activity
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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. -
Kostik replied to the thread A A global energy conservation law in general relativity.Thanks. I’m in the airport lounge in Istanbul, changing planes on the way to Tashkent. I will digest this later and probably revisit...
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Kostik replied to the thread A A global energy conservation law in general relativity.You can ignore the pseudotensor, that’s a distraction. Just consider the ##Y## term and focus on global conservation of...
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Kostik replied to the thread A A global energy conservation law in general relativity.He certainly does. See the photo in #3 above.
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Kostik replied to the thread A A global energy conservation law in general relativity.Thanks, I will digest later when I have the time. Note that Dirac used harmonic coordinates only in Ch 33-34 on gravitational waves...
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Kostik replied to the thread A A global energy conservation law in general relativity.@weirdoguy Energy density ##T^{00}\sqrt{-g}## is not a scalar density … but one component of a rank-2 tensor density.
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Kostik replied to the thread A A global energy conservation law in general relativity.It just occurred to me — how does Dirac integrate a tensor density over a volume? A scalar density — yes; but a vector density or a...
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Kostik replied to the thread A A global energy conservation law in general relativity.Dirac’s book is easily found on the internet, see here: https://lib.undercaffeinated.xyz/get/pdf/4188 Pp. 45-46 explain the...
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Kostik replied to the thread A A global energy conservation law in general relativity.As I said, he gives a very clear explanation.
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Kostik replied to the thread A A global energy conservation law in general relativity.I don't think that is right. Dirac gives a very clear explanation why ##T^{\mu\nu}\sqrt{-g}## is the density of energy-momentum in...
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Kostik replied to the thread A A global energy conservation law in general relativity.Never mind the pseudotensor; that's a distraction. My question concerns whether the mixed tensor ##T^0_{\, 0}\sqrt{-g}## represents (in...
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Kostik replied to the thread A A global energy conservation law in general relativity.You're saying that ##T^{00}\sqrt{-g}## and ##T^0_{\,0}\sqrt{-g}## both represent the energy density (in curved spacetime)? But they're...
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Kostik replied to the thread A A global energy conservation law in general relativity.Dirac seems to disagree. Here he is discussing the energy-momentum pseudotensor ##{t_\mu}^\nu##, and ##{Y_\mu}^\nu## is just the mixed...
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Kostik posted the thread A A global energy conservation law in general relativity in Special and General Relativity.Please see the derivation below that, if the metric is time-independent, then the integral over a sufficiently large 4D spacetime region...
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Kostik replied to the thread A Weinberg's proof of ##{T^{\mu\nu}}_{,\nu}=0## for a perfect fluid.Of course; thanks. I think I have found another proof, but I should have seen this.
