## Divergence of Energy-momentum Tensor

How do you prove that Maxwell's energy-momentum equation is divergence-free?
I don't know whether or not I have to use Lagrangians or Eistein's tensor, or if there's a simlpler way of expanding out the tensor..

∂$_{\mu}$T$^{\mu\nu}$=0

T$^{}\mu\nu$=F$^{}\mu\alpha$F$^{}\nu$$_{}\alpha$-1/4F$^{}\alpha\beta$F$_{}\alpha\beta$$\eta$$^{}\mu\nu$

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 I mean ∂$_{\mu}$T$^{\mu\nu}$=0 T$^{\mu\nu}$=F$^{\mu\alpha}$F$^{\nu}$$_{\alpha}$-1/4F$^{\alpha\beta}$F$_{\alpha\beta}$$\eta$$^{\mu\nu}$
 Recognitions: Gold Member Homework Help Science Advisor Staff Emeritus Try writing $F_{\mu\nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$ and using the commutativity of the derivatives.

 Tags divergence, energy, momentum, relativity, tensor