Solution
= Solution
$G_{\mu\nu}=R_{\mu\nu}-\tfrac12Rg_{\mu\nu}$. The contracted Bianchi identity $\nabla^\mu G_{\mu\nu}=0$ is required to match $\nabla^\mu T_{\mu\nu}=0$.
= Solution
$G_{\mu\nu}=R_{\mu\nu}-\tfrac12Rg_{\mu\nu}$. The contracted Bianchi identity $\nabla^\mu G_{\mu\nu}=0$ is required to match $\nabla^\mu T_{\mu\nu}=0$.