On light-like extremal surfaces in curved spacetimes

TL;DR

This paper studies light-like extremal surfaces in curved spacetimes, especially Schwarzschild spacetime, revealing their description via nonlinear geodesic equations and deriving new solutions to compare with existing results.

Contribution

It introduces a novel approach to describe light-like extremal surfaces through nonlinear geodesic equations and systematically derives new solutions in Schwarzschild spacetime.

Findings

Light-like extremal surfaces can be described by nonlinear geodesic equations.

New special solutions in Schwarzschild spacetime are systematically derived.

The method provides a way to compare with known solutions and explore surface properties.

Abstract

In this paper, we are concerned with light-like extremal surfaces in curved spacetimes. It is interesting to find that under a diffeomorphic 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 comparing with the known results and illustrating the method.