Hi everyone!(adsbygoogle = window.adsbygoogle || []).push({});

I'm having a lillle problem proving that the einstein tensor is divergence free!!

I don't know how to begin, i start with

[tex]\nabla_\mu G^{\mu\nu}=\nabla_{\mu}(R^ {\mu\nu} -\frac{1}{2}g^{\mu\nu}R)[/tex]

i tried to do [tex]\nabla_\mu G^{\mu\nu}=\nabla_{\mu}g^{\mu\nu}(g_{\mu\nu}R^{\mu\nu}-\frac{1}{2}R)[/tex]

(by the way, is that right? I guess no becaouse then I get to [tex]g^{mu\nu}(\nabla_{\mu}(R-\frac{1}{2}R))=\frac{1}{2}g^{\mu\nu}\frac{\partial R}{\partial \mu}[/tex] which i guess never goes to zero!)

can you help me out?

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# Einstein's tensor divergence

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