The Analysis of the Black Hole Interior and Strong Cosmic Censorship

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.