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[tex]L_{BI}=1 - \sqrt{ 1+\frac{1}{2}F_{\mu\nu }F^{\mu\nu}-\frac{1}{16}\left(F_{\mu\nu}\widetilde{F}^{\mu\nu} \right)^{2}}[/tex]

with [itex]G^{\mu\nu}=\frac{\partial L}{\partial F_{\mu\nu}}[/itex] how can we show that in empty space the equations of motion take the form [itex]\partial_{\mu}G^{\mu\nu}=0[/itex]

We should start with an Euler-Lagrange equation, but how can i write it for this Lagrangian?