2020/03/12 by Ethan Yale. Jaffe, Jaffe, Ethan Yale, Ethan Yale Jaffe
Physics and Astronomy · #35Q76 #Advanced Differential Geometry Research #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2003.05985
openalex publication_date 2020/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this thesis we present partial progress towards the dynamic formation of\nblack holes in the four-dimensional Einstein vacuum equations from\nChristodoulou's short-pulse ansatz. We identify natural scaling in a putative\nsolution metric and use the technique of real blowup to propose a\ndesingularized manifold and an associated rescaled tangent bundle (which we\ncall the "short-pulse tangent bundle") on which the putative solution remains\nregular. We prove the existence of a solution solving the vacuum Einstein\nequations formally at each boundary face of the blown-up manifold and show that\nfor an open set of restricted short-pulse data, the formal solution exhibits\ncurvature blowup at a hypersurface in one of the boundary hypersurfaces of the\ndesingularized manifold.\n This thesis is intended to be partially expository. In particular, this\nthesis presents an exposition of double-null gauges and the solution of the\ncharacteristic initial value problem for the Einstein equations, as well as an\nexposition of a new perspective of Christodoulou's monumental result on the\ndynamic formation of trapped surfaces.\n