Mathematical problems in gravitational collapse

引力塌缩中的数学问题

• 批准号: 2882490
• 金额: --
• 依托单位: University of Cambridge
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2882490
• 关键词: Mathematical; problems; gravitational; collapse

The thesis project involves understanding basic science questions concerning gravitational collapse of isolated systems in general relativity. Problems to be addressed include the issue of critical collapse, the cosmic censorship conjectures and the instability of naked singularities, the relevance of shock formation in self-gravitating fluids, and the nature of singularities inside black holes. These questions have precise mathematical formulations and can be addressed using the qualitative theory of partial differential equations. The thesis will build on many recent mathematical advances in the field over the past few years, including advances in the mathematical technology for handling the Einstein equations of general relativity and the Euler equations of fluid mechanics in non-trivial geometric settings

论文项目涉及理解广义相对论中孤立系统引力坍缩的基础科学问题。要解决的问题包括临界坍缩问题，宇宙审查机制和裸奇点的不稳定性，自引力流体中激波形成的相关性，以及黑洞内部奇点的性质。这些问题有精确的数学公式，可以用偏微分方程的定性理论来解决。本论文将建立在过去几年该领域的许多最新数学进展的基础上，包括在处理广义相对论的爱因斯坦方程和非平凡几何设置的流体力学的欧拉方程的数学技术的进展