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$\begingroup$ Thanks, really nice answer - I haven't seen the trick involving the projection onto the orthogonal compliment of u before. So summarising, the total stress-energy tensor must be divergence free to locally conserve 4-momentum. And you have explicitly shown for EM & dust in curved spacetime, 4-momentum in the stress energy tensor must match the 4-momentum in the Lorentz law, otherwise 4-momentum is transferred between dust and EM field at different rates. $\endgroup$

KierD
– KierD

2025-12-03 11:33:52 +00:00
Commented 21 hours ago

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