On Light-Like Extremal Surfaces in Curved Spacetimes

In this paper,we are concerned with light-like extremal surfaces in curved spacetimes.It is interesting to find that under a difeomorphic transformation of variables,the light-like extremal surfaces can be described by a system of nonlinear geodesic equations.Particularly,we investigate the light-like extremal surfaces in Schwarzschild spacetime in detail and some new special solutions are derived systematically with aim to compare with the known results and to illustrate the method.