Snell’s law for the Schwarzschild black hole

Abstract

The Wheeler equation, for electromagnetic disturbances in a gravitational field, was found by Fiziev to have exact solutions both above and below the event horizon, in the form of waves propagating both inwardly and outwardly. This observation can be interpreted and verified from the optical point of view, entirely on the basis of the Schwarzschild metric for length contraction and time dilation, in order to derive a differential version of Snell's law for the Schwarzschild black hole. It reveals interesting physics, including the correct amount of light deflection by the Sun, internal and external Oppenheimer-Snyder cones of the black hole, properties of its phonon sphere and the conclusion that light-rays are kept below the horizon by length contraction and time dilation rather than deflection.