Singularity theorems and the [General Relativity + additional matter fields] formulation of metric theories of gravitation

Abstract

By using the [General Relativity + additional matter fields] formulation (which depends on a redefined metrich μν ) of metric theories of gravitation, the study of singularities characterized by incomplete nonspacelike geodesics is simplified, but may be used only if (at least) the non-spacelike geodesics of the original metricg μν are conserved under the transformation betweeng μν and the new metrich μν . In order that every class of geodesies of a diagonal Bianchi I metric correspond to the same class of geodesies of a diagonal metrich μν , it is necessary that the transformation between these two metrics be a constant (positive) conformal transformation. We analyse the implications of the previous results for the singularitiesg μν when the latter is a solution of theories with a quadratic or polynomial Lagrangian.