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

TL;DR

This paper investigates the initial data constraints on the light cone in the Einstein-Vlasov system, addressing gauge issues, solving constraints globally, and analyzing data behavior at the cone's vertex.

Contribution

It provides a detailed derivation and resolution of initial data constraints on the light cone for the Einstein-Vlasov system, including gauge preservation and data behavior analysis.

Findings

Derived Gauss-Codazzi constraints on the light cone.

Established gauge-preservation for the constraints.

Identified classes of initial data sets from free data.

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.