The cosmological problem as initial value problem on the observer's past light cone: geometry

Abstract

In the context of general relativity an approach to cosmology is suggested which rests exclusively on quantities accessible to the astronomical observer. The approach is based on the characteristic initial value problem for the Einstein field equations imposed on the observer's past light cone. the inner geometry of the past light cone enters the relations between observable quantities. Thus, it should become possible to determine both the cone geometry, as well as the distribution of cosmic matter near the cone, without adopting arbitrary assumptions. The propagation equations determine the gravitational field and the matter distribution at finite distances from the past cone. The author specifies the cone initial data for a general dust model. An explicit procedure in terms of successive integrations is given to determine the gravitational field near the past light cone.