Minkowski space is shown to be globally stable as a solution to the massive Einstein–Vlasov system. The proof is based on a harmonic gauge in which the equations reduce to a system of quasilinear wave equations for the metric, satisfying the weak null condition, coupled to a transport equation for the Vlasov particle distribution function. Central to the proof is a collection of vector fields used to control the particle distribution function, a function of both spacetime and momentum variables. The vector fields are derived using a general procedure, are adapted to the geometry of the solution and reduce to the generators of the symmetries of Minkowski space when restricted to acting on spacetime functions. Moreover, when specialising to the case of vacuum, the proof provides a simplification of previous stability works.

中文翻译：

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调和规范中爱因斯坦-弗拉索夫系统的闵可夫斯基空间的全局稳定性

作为大规模爱因斯坦-弗拉索夫系统的解决方案，闵可夫斯基空间被证明是全局稳定的。该证明基于谐波规范，其中方程简化为度量的拟线性波动方程系统，满足弱零条件，耦合到 Vlasov 粒子分布函数的传输方程。证明的核心是用于控制粒子分布函数的向量场集合，粒子分布函数是时空和动量变量的函数。矢量场是使用一般程序导出的，适用于解的几何形状，并在限制作用于时空函数时简化为 Minkowski 空间对称性的生成元。此外，当专门研究真空的情况时，证明提供了以前稳定性工作的简化。