Generalizing Optical Geometry

We generalize the optical geometry to include, not only conformally static spacetimes, but any spacetime that admits a hypersurface orthogonal shearless congruence of worldlines. In the generalized optical geometry, which in general is time dependent, photons move with constant speed along spatial geodesics. Gyroscopes moving along spatial geodesics do not precess. We also classify inertial forces within this framework. For a Schwarzschild black hole the generalized optical geometry works from infinity, across the horizon and arbitrarily close to the singularity.