MATHEMATICAL PROBLEMS IN GENERAL RELATIVITY

该项目旨在研究爱因斯坦方程的各个方面，这些方程支配广义相对论中时空几何的动态。PI特别感兴趣的是研究重力非常强的解决方案，包括时空奇点的存在，以及物质场（如恒星和气体）与重力之间存在强烈相互作用的设置。 更广泛的影响包括与学生的工作，该项目提出了一些问题，被认为是研究生的研究准备。PI试图回答这个项目中的一系列问题。一般黑洞的奇异边界是什么样子的？当存在物质场时，奇异边界会发生什么？奇异边界附近的物质场本身会发生什么？物质场的自引力“零壳层”如何传播和相互作用？在自引力气体中激波是如何形成的？在解决这些问题的同时，PI还将开发适用于广义相对论之外的双曲型偏微分方程的数学工具。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The project aims at studying various aspects of the Einstein equations, which govern the dynamics of spacetime geometry in general relativity. The PI is particularly interested in studying the solution regimes where gravity is very strong, including in the presence of spacetime singularities, as well as settings where there is a strong interaction between matter fields (such as stars and gases) and gravity. Broader impacts include work with students, and the project presents some questions that are believed to be ready for research by graduate students.THe PI seeks to answer a series of questions in this project. What does the singular boundary of generic black holes look like? What happens to the singular boundary when matter fields are present, and what happens to the matter fields themselves near the singular boundary? How do self-gravitating "null shells of matter fields propagate and interact? How does shock form in self-gravitating gas? While solving these problems, the PI will develop mathematical tools useful for hyperbolic partial differential equations beyond the application in general relativity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.