The Analysis of the Black Hole Interior and Strong Cosmic Censorship

广义相对论是引力的基本理论，支配着从宇宙诞生到恒星命运的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，吸引了公众的想象力，仍然是广义相对论最显着的预测之一。虽然天体物理学通过探测黑洞的引力波（LIGO合作）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？“该项目支持基于爱因斯坦方程数学研究的研究计划，这将大大有助于我们在广义相对论框架内理解黑洞内部。该项目的工作预计将产生广泛的影响，不仅在天体物理学，而且在我们探索引力的基本性质。该项目为研究生提供了研究培训机会。罗杰·彭罗斯（Roger Penrose）因其1965年的奇点定理获得2020年诺贝尔物理学奖，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拥有巨大的天体物理学兴趣，而且与深刻的理论问题有关，例如强宇宙审查猜想，它肯定了广义相对论的确定性特征。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，这一过程导致了黑洞。通过开展一系列建立在球对称模型上的项目，这项研究奋进为实现这一目标做出了重大贡献，更广泛地说，推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NSF的法定使命，并通过使用基金会的智力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.