The Cauchy problem in general relativity. I. Metrics containing arbitrary functions

This paper develops a Lagrangian formalism (the yA−formalism) for use in investigating the Cauchy problem in general relativity. In particular it will be used in a subsequent paper to present a Lagrangian formulation of the characteristic initial−value problem in general relativity. The formalism enables one to define ’’field equations’’ and ’’Bianchi identities’’ for metrics containing arbitrary functions in the case when the arbitrary functions are treated as the field variables.