On the Initial Data Constraints on the Light cone for the Einstein-Vlasov system

Abstract

This article is concerned with the derivation of the Gauss-Codazzi's constraints equations on the initial light cone for geometric transport equations in general relativity. Temporal-gauge-dependent constraints are addressed too and gauge-preservation is established. The global resolution of the constraints is studied, a large class of initial data sets is deduced from appropriate free data and their behavior at the vertex of the cone is examined.