Beyond Stability of Black Holes in General Relativity

该项目致力于回答广义相对论中有关强场动力学的基本问题，包括黑洞过程和时空奇点的形成和结构。这些问题可以用数学来表达，该项目将有助于严格的数学对我们的物理世界做出基本陈述的古老传统，从长远来看，这一传统已被证明是科学和技术进步的核心。黑洞和时空奇点的主题激发了科学界之外的大众想象力，这一点从公众对双黑洞系统引力波探测的接受以及最近超大质量黑洞附近的第一张令人惊叹的图像中可以明显看出。 本项目的主要研究者和共同研究者还将通过对博士生进行与本项目研究相关问题的培训，为更广泛的影响做出贡献。本项目致力于超越广义相对论稳定性问题的研究，并回答有关该理论强场动力学的基本问题，包括引力散射的非线性方面，引力辐射的精细结构和时空奇点的性质。该项目的第一个主要目标是，基于一系列先前的联合工作，完成Kerr黑洞度规的非线性稳定性的数学证明。 该项目的第二个主要目标是了解黑洞内部时空奇点的结构，旨在了解它们的一般形式，特别是它们最终是否变得强大和类空。第三个也是最后一个主要的目标是关于真空中是否存在不隐藏在黑洞中的奇点的问题。该项目旨在肯定地回答这个问题，同时调查这些奇点的稳定性。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。

This project strives to answer fundamental questions about strong field dynamics in general relativity, including black hole processes and the formation and structure of spacetime singularities. These questions can be expressed in mathematics and the project will contribute to the venerable tradition of rigorous mathematics making fundamental statements about our physical world, a tradition which in the long run has proven central to advances in science and technology. The subject of black holes and spacetime singularities has inspired the popular imagination well beyond the confines of the scientific community, as was apparent in the public reception of the detection of gravitational waves from binary black hole systems and, most recently, of the first stunning images of the immediate vicinity of a supermassive black hole. The PI and co-PI will also contribute to broader impacts via training of PhD students on problems related to the research in this project.This project strives to advance beyond the study of stability problems in general relativity and answer fundamental questions about strong field dynamics of the theory, including non-linear aspects of gravitational scattering, the fine structure of gravitational radiation and the nature of spacetime singularities. The first major objective of this project, based on a long sequence of previous joint work of the proposers, is to finish up the mathematical proof of the non-linear stability of the Kerr black hole metric. The second major objective of this project concerns understanding the structure of spacetime singularities inside black holes, aiming to understand their general form, in particular, whether they eventually become strong and spacelike. A third and final major objective concerns the question of whether singularities exist in the vacuum which are not hidden in black holes. The project aims to answer this question in the affirmative, investigating also the stability of these singularities.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.