Show charge conservation in a curved spacetime

Actually, I think I made a mistake. That formula is just the trace of the Christoffel symbol. But it does lead to a simpler proof of the formula you're trying to prove. Let me write it up and I'll post it.In summary, we can use the antisymmetry of ##F^{ab}## and the identities ##\nabla_a J^a = \frac{1}{\sqrt{|g|}} \partial_a \left( \sqrt{|g|} J^a \right)## and ##\nabla_a F^{ab} = \frac{1}{\sqrt{|g|}} \partial_a \left( \sqrt{|g|} F^{ab}
  • #36
If you like the abstract calculus with forms, there's a textbook about electromagnetism, which may be interesting for you:

F. W. Hehl, Y. N. Obukhov, Foundations of classical electrodynamics, Springer (2003)
 
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  • #37
Thanks, I'll check that one out! Another nice book I found that teaches similar mathematics is 'Gauge Fields, Knots and Gravity' by John Baez, which is very cool :smile:
 
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