CAREER: Singularity Formation in Dynamical Black Holes

Black holes are among the most striking predictions of Einstein’s theory of gravity, yet their interior region remains one of the greatest mysteries in mathematical physics. This project investigates the mathematics governing these regions of spacetime characterized by extreme gravity. By developing new mathematical frameworks to analyze the interior of black holes, this research serves the national interest and the National Science Foundation's mission to advance our fundamental understanding of the universe. Furthermore, the project yields broad societal benefits by heavily investing in STEM education across multiple levels. The principal investigator leads outreach initiatives connecting high school students with active researchers, develops resources for the undergraduate curriculum linking differential equations to physical applications, and organizes scientific events and training opportunities for graduate students and early-career researchers. The primary goal of this project is to rigorously establish the dynamic formation and nature of singularities in generic black hole solutions to the Einstein equations. The research relies on advanced techniques in nonlinear hyperbolic partial differential equations combined with Lorentzian Geometry, with a specific focus on the global singularity structure in the black hole interior during the process of gravitational collapse outside of symmetry assumptions. These advancements yield crucial steps toward resolving the celebrated Strong Cosmic Censorship Conjecture in General Relativity, while simultaneously providing multiple accessible problems suitable for student research at the undergraduate and graduate levels, and leveraging the widespread public fascination with black holes to drive engaging educational and outreach initiatives. 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. NSF Award ID: 2541031 | Program: 01002930DB NSF RESEARCH & RELATED ACTIVIT,01003031DB NSF RESEARCH & RELATED ACTIVIT,01002627DB NSF RESEARCH & RELATED ACTIVIT | Principal Investigator: Maxime Van de Moortel | Institution: Rutgers University New Brunswick, NEW BRUNSWICK, NJ | Award Amount: $259,277 View on NSF Award Search: https://www.nsf.gov/awardsearch/show-award/?AWD_ID=2541031 View on Research.gov: https://www.research.gov/awardapi-service/v1/awards/2541031.html