LIGHT CONE CUT SOLUTION IN THE 2+1 NULL SURFACE FORMULATION

The null surface formulation of general relativity differs from the standard approach by featuring the light cone cut at null infinity as the prominent variable, rather than the metric tensor. In this paper, an example of such a light cone cut is constructed by integrating the null geodesic equations for an asymptotically flat (2+1)-dimensional spacetime with a smooth matter source. The formula for the light cone cut is presented both parametrically and also explicitly as a function u = Z(x^a; φ) where u and φ are the Bondi coordinates of future null infinity, I⁺. The cut u is shown to be a simple closed curve.