Null cones in Schwarzschild geometry

Abstract

In this work we investigate aspects of light cones in a Schwarzschild geometry, making connections to gravitational lensing theory and to a new approach to general relativity, the null surface formulation. By integrating the null geodesics of our model, we obtain the light cone from every space-time point. We study three applications of the light cones. First, by taking the intersection of the light cone from each point in the space-time with null infinity, we obtain the light cone cut function, a four parameter family of cuts of null infinity, which is central to the null surface formulation. We examine the singularity structure of the cut function. Second, we give the exact gravitational lens equations, and their specialization to the Einstein ring. Third, as an application of the cut function, we show that the recently introduced coordinate system, the “pseudo Minkowski” coordinates, are a valid coordinate system for the space-time