The Analysis of the Black Hole Interior and Strong Cosmic Censorship

广义相对论是引力的基本理论，它支配着从宇宙的诞生到恒星的命运等天体物理现象的行为。这个理论的核心是爱因斯坦方程，它决定了时空的结构。值得注意的是，黑洞的存在，吸引着公众的想象力，仍然是广义相对论最引人注目的预言之一。虽然天体物理学通过探测引力波（LIGO合作）为黑洞提供了令人信服的观测证据，但一个基本问题仍然存在：“黑洞内部是什么？”该项目支持一个基于爱因斯坦方程数学研究的研究项目，这将大大有助于我们在广义相对论的框架内理解黑洞的内部。该项目的工作不仅在天体物理学方面，而且在我们对引力基本性质的探索方面都有望产生广泛的影响。本项目为研究生提供研究训练机会。罗杰·彭罗斯（Roger Penrose）因1965年提出奇点定理而获得2020年诺贝尔物理学奖，他最近强调了黑洞内部在广义相对论中的重要性。这些神秘的区域不仅引起了巨大的天体物理学兴趣，而且与一些深刻的理论问题有关，比如肯定广义相对论确定性特征的强宇宙审查猜想。该项目旨在对黑洞内部的爱因斯坦方程进行数学分析，最终目标是在引力坍缩的背景下为难以捉摸的强宇宙审查猜想提供严格的证明，引力坍缩是产生黑洞的过程。通过开展一系列建立在球对称模型上的项目，本研究努力为实现这一目标做出了重大贡献，更广泛地说，促进了我们对广义相对论中奇点形成和稳定性机制的理解。该奖项反映了美国国家科学基金会的法定使命，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。

General Relativity stands as the fundamental theory of gravity, governing the behavior of astrophysical phenomena ranging from the birth of the universe to the fate of stars. Central to this theory are the Einstein equations, which determine the structure of spacetime. Notably, the existence of black holes, captivating the public's imagination, remains one of the most remarkable predictions of General Relativity. While Astrophysics has provided compelling observational evidence of black holes through the detection of their gravitational waves (LIGO collaboration), a fundamental question persists: "What lies within the interior of a black hole?" This project supports a research program based on the mathematical study of the Einstein equations, which will significantly contribute to our understanding of the interior of black holes within the framework of General Relativity. The work of the project is expected to have broad implications, not only in Astrophysics but also in our exploration of the fundamental nature of gravity. The project provides research training opportunities for graduate students.The 2020 Physics Nobel Prize of Roger Penrose, attributed to his 1965 singularity theorem, recently highlighted the importance of the interiors of black holes within General Relativity. These enigmatic regions not only hold immense astrophysical interest but also bear relevance to profound theoretical questions such as the Strong Cosmic Censorship conjecture, which affirms the deterministic character of General Relativity. This project is aimed at the mathematical analysis of the Einstein equations within the interior of black holes, with the ultimate objective of providing a rigorous proof of the elusive Strong Cosmic Censorship Conjecture within the context of gravitational collapse, the process giving rise to black holes. By conducting a series of projects building up on spherically symmetric models, this research endeavor significantly contributes towards this goal and, more broadly, advances our understanding of the mechanisms governing the formation and stability of singularities within 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.