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generalization of Einstein mass-energy relation to Field-full Curved spacetime ?

Widdekind
in Relativity

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working backwards, from the Klein-Gordon equation...

 

is the generalized mass-energy relation, for curved spacetime, full of EM fields:

 

[math]\left(P - e A\right)^{\mu} g_{\mu \nu} \left( P - e A \right)^{\nu} = m^2[/math]

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