- #1
ClaraOxford
- 6
- 0
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..
∂[itex]_{\mu}[/itex]T[itex]^{\mu\nu}[/itex]=0
T[itex]^{}\mu\nu[/itex]=F[itex]^{}\mu\alpha[/itex]F[itex]^{}\nu[/itex][itex]_{}\alpha[/itex]-1/4F[itex]^{}\alpha\beta[/itex]F[itex]_{}\alpha\beta[/itex][itex]\eta[/itex][itex]^{}\mu\nu[/itex]
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..
∂[itex]_{\mu}[/itex]T[itex]^{\mu\nu}[/itex]=0
T[itex]^{}\mu\nu[/itex]=F[itex]^{}\mu\alpha[/itex]F[itex]^{}\nu[/itex][itex]_{}\alpha[/itex]-1/4F[itex]^{}\alpha\beta[/itex]F[itex]_{}\alpha\beta[/itex][itex]\eta[/itex][itex]^{}\mu\nu[/itex]