2014/09/22 by Xinliang An, An, Xinliang, Jonathan Luk +1 · 1 citation
Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Quantum Electrodynamics and Casimir Effect
paper · pdf · doi:10.48550/arxiv.1409.6270
openalex publication_date 2014/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study the "minimal requirement" on the incoming radiation that guarantees a trapped surface to form in vacuum. First, we extend the region of existence in Christodoulou's theorem on the formation of trapped surfaces and consequently show that the lower bound required to form a trapped surface can be relaxed. Second, we demonstrate that trapped surfaces form dynamically from a class of initial data which are large merely in a scaling-critical norm. This result is motivated in part by the scaling in Christodoulou's formation of trapped surfaces theorem for the Einstein-scalar field system in spherical symmetry.