Solving $ R_{uv} - g^{00}A e^{-r^2}g_{uv} = 0$ in spherical coordinates

Question

How to solve this tensor equation, $ R_{uv} - g^{00}A e^{-r^2}g_{uv} = 0$ in spherical coordinates ?

Where $R_{uv}$ is Ricci tensor ,$ g_{uv} $ is metric tensor, $ A $ a constant, $ r $ is radius in spherical coordinates.