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.

本文关注的是广义相对论中考虑时间规范时几何输运方程的初始光锥上的柯西问题。突出显示了一种新的特征初始数据约束层次结构，其中包括标准 Gauss Codazzi 约束方程和时间规范相关约束，并建立规范保存。研究了约束的全局分辨率，从合适的自由数据推导出一大类初始数据集，并检查它们在锥体顶点的行为。对于光锥上光滑函数引起的初始数据，在锥尖附近建立了爱因斯坦-弗拉索夫系统的短时解。