Einstein equations in the null quasispherical gauge

Abstract

Properties of the Einstein equations in a coordinate gauge based on expanding null hypersurfaces foliated by metric 2-spheres are described. This null quasispherical (NQS) gauge leads to particularly simple analyses of the characteristic structure of the equations and of the propagation of gravitational shocks, and clarifies the geometry of timelike boundary condition. A feature of the NQS gauge is the use of the standard (`edth') operator on to express angular derivatives, and the consequent use of spin-weighted spherical harmonic decompositions of the metric fields.