Past exam of the mathematics course of the University of Cambridge / 2010 / iii / Paper 52 / 1 / c / Solution

No: the theory predicts zero gravitational deflection of light. The reason is conformal preservation of null geodesic paths. Along a null geodesic with tangent $k^i$, the geodesic equation for a conformally flat metric reduces tobecause ${\eta }_{ij}{k}^i{k}^j=0$. The acceleration is parallel to the tangent and changes only its parametrization. Equivalently, with ${\ell }^i={\varphi }^2{k}^i$, $d{\ell }^i/d\lambda =0$, so the unparametrized ray is a straight null geodesic of Minkowski spacetime. A positive conformal factor also preserves local angles, so this straight-path result cannot be hidden by changing the local angle measurement. It contradicts the nonzero solar deflection observed in gravitational lensing, while remaining compatible with the gravitational redshift in part (b).