Conformal rigidity from focusing

The null curvature condition (NCC) is the requirement that Ricci of a Lorentzian manifold be nonnegative along directions, which ensures focusing geodesic congruences. In this note, we show NCC together with causal structure significantly constrain metric. particular, prove any conformal rescaling vacuum spacetime introduces either incompleteness or negative curvature, provided factor non-constant on at least one complete geodesic. context bulk reconstruction in AdS/CFT, our results combined technique light-cone cuts can used spacetimes to reconstruct full metric regions probed by geodesics reaching boundary. For non-vacuum spacetimes, factor, giving an approximate