The Cauchy problem in general relativity. II. Main and constraint equations in the characteristic initial−value problem

Abstract

This paper applies the ’’yA−formalism’’ of a previous paper (Paper I) to a Lagrangian formulation of the characteristic initial−value problem in general relativity. The essential content of the paper is the respective identifications of the ’’field equations’’ and ’’Bianchi identities’’ of the yA−formalism with the ’’main equations’’ and ’’constraint equations’’ of a metric in a Bondi coordinate system. The identifications are developed in detail in the case of Bondi’s (axially symmetric) radiating metric.