Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 37E / a / Solution

In the static limit, the supplied linearized Riemann tensor givesThe trace of the Einstein field equations is $R=-\kappa T$. Here $T\simeq -\rho$, so $R=\kappa \rho$. The $00$ field equation is thereforewhich yields $R_{00}=\kappa \rho /2$. Combining the two expressions for $R_{00}$ gives