Einstein equations in the null quasi-spherical gauge

TL;DR

This paper analyzes the Einstein equations in a null quasi-spherical gauge, revealing their structure and applications in boundary conditions, matching problems, and shock propagation in general relativity.

Contribution

It introduces a simplified form of Einstein equations in a null quasi-spherical gauge and explores their applications in boundary conditions, matching, and shock propagation.

Findings

Simplified Einstein equations in null quasi-spherical gauge

Application to boundary conditions and matching problems

Insights into gravitational shock propagation

Abstract

The structure of the full Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres is explored. The simple form of the resulting equations has many applications -- in the present paper we describe the structure of timelike boundary conditions; the matching problem across null hypersurfaces; and the propagation of gravitational shocks.