Characteristic Cauchy problem on the light cone for the Einstein–Vlasov system in temporal gauge

Abstract

This article is concerned with the Cauchy problem on the initial light cone for geometric-transport equations in general relativity when temporal gauge is considered. A novel hierarchy of characteristic initial data constraints is highlighted which includes the standard Gauss Codazzi’s constraints equations and temporal-gauge-dependent constraints, and gauge-preservation is established. The global resolution of the constraints is studied, a large class of initial data sets is deduced from suitable free data and their behavior at the vertex of the cone is examined. For initial data induced by smooth functions on the light cone, a short time solution is established for the Einstein–Vlasov system in a neighborhood of the tip of the cone.