>> A Lorentizian manifold looks locally hyperbolic, so we need to imagine a light cone. Now the curvature of this manifold tells us how we need to distort light

>> A Lorentizian manifold looks locally hyperbolic, so we need to imagine a light cone. Now the curvature of this manifold tells us how we need to distort light cones at different points to build up the full space. > A Lorentzian manifold is not necessarily locally hyperbolic Maybe OP was thinking of some local notion of global hyperbolicity[0] (which, of course, has nothing to do with hyperbolic Riemannian manifolds)? [0] https://en.wikipedia.org/wiki/Globally_hyperbolic_manifold https://en.wikipedia.org/wiki/Globally_hyperbolic_manifold