Light-Cone Coordinate System in General Relativity

TL;DR

This paper discusses the structure and construction of light-cone coordinate systems in general relativity, highlighting their properties and applications in simplifying Einstein's field equations and astrophysical calculations.

Contribution

It provides a detailed analysis of conditions for existence and methods to construct light-cone coordinate systems in space-time.

Findings

Derived conditions for light-cone coordinate system existence

Presented methods to construct these coordinates from standard ones

Explained geometrical and physical interpretations with examples

Abstract

If there is a null gradient field in 1+3 dimensional space-time, we can set up a kind of light-cone coordinate system in the space-time. In such coordinate system, the metric takes a simple form, which is much helpful for simplifying and solving the Einstein's field equation. This light-cone coordinate system has wonderful properties and has been widely used in astrophysics to calculate parameters. In this paper, we give a detailed discussion for the structure of space-time with light-cone coordinate system. We derive the conditions for existence of such coordinate system, and show how to construct the light-cone coordinate system from usual ones, then explain their geometrical and physical meanings by examples.