Homework Statement
Hi all, I currently have a modified Einstein-Hilbert action, with extra terms coming from some vector field A_\mu = (A_0(t),0,0,0), given by
\mathcal{L}_A = -\frac{1}{2} \nabla _\mu A_\nu \nabla ^\mu A ^\nu +\frac{1}{2} R_{\mu \nu} A^\mu A^\nu .
The resulting field...