Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 309 / 3 / b / ii / Solution

For Minkowski spacetime, $R_{ab}=0$ and $R=0$, while $f^{\prime }(R)$ is constant. In vacuum $T_{ab}=0$, so every derivative term vanishes and the remaining term is $-\frac{1}{2}{\eta }_{ab}f(0)=0$. Hence Minkowski spacetime is a vacuum solution of this modified gravity theory.