Density and Positive Mass Theorems for Black Holes and Incomplete Manifolds

Watch a technical mathematics lecture from the General Relativity Workshop where Princeton researcher Ryan Unger presents groundbreaking work on density theorems for Einstein constraint equations with marginally outer trapped boundaries. Explore the generalization of density theorems by Corvino-Schoen and Eichmair-Huang-Lee-Schoen, examining their application to apparent horizons in black holes. Discover how this research resolves the spacetime positive mass theorem for non-spin cases with MOTS boundary, while also revealing unexpected implications for Riemannian manifolds, including insights into negative mass manifolds. Learn about collaborative findings with Martin Lesourd and Dan Lee that advance our understanding of black holes and incomplete manifolds in general relativity.