Quote by pervect, mine text is red:
You'll need to clarify a bit. It sounds like you are asking for the null geodesics (the paths that light follow) given the metric of spacetime (g_ij). not just g_ij However, you need to specify the velocity as well as its position to calculate the geodesic. exactly, so I said: on step k, we're in x_i, with 'velocity' dx_i (=dt,i=4) ...if I'm understanding it correctly, because while geodesic deviation will cause light beams to "curve", that curvature is equivalent ot an acceleration, and it won't affect the velocity of light (which after all is always equal to 'c' locally). that is, in tangent euclidean coordinates, but x_i I am speaking about, are distant static observer ones

(there must be simple iterative solution)