Gravitating relativistic material bodies: A mathematical analysis

该项目旨在建立代表引力相对论物质体系统的爱因斯坦-弹性方程解的局部时间存在性和几何唯一性，并了解这些解的长期行为。尽管它们对天体物理学很重要，但对于控制相对论性物体引力系统的运动方程的解的数学性质，几乎一无所知。该项目将为研究引力相对论性物质体提供数学工具，并为制定模拟的稳定数值方案提供指导，这对于将理论与实验进行比较至关重要。这将极大地改善目前对物体物质真空边界附近物质和引力场行为的理解，并有助于理解这些边界的物理学。

This project aims to establish the local-in-time existence and geometric uniqueness of solutions to the Einstein-Elastic equations representing systems of gravitating relativistic material bodies, and to understand the long-time behaviour of these solutions. In spite of their importance to astrophysics, almost nothing is known about the mathematical properties of solutions to the equations of motion governing gravitating systems of relativistic material bodies. This project would provide mathematical tools for the study of gravitating relativistic material bodies and provide guidance on developing stable numerical schemes for simulations that are essential for comparing theory with experiment. This would significantly improve current understanding of the behaviour of matter and gravitational fields near the matter-vacuum boundary of bodies and help understanding of the physics of these boundaries.