Asymptotic description of the formation of black holes from short-pulse data
Author(s)Jaffe, Ethan Yale.
Massachusetts Institute of Technology. Department of Mathematics.
Richard B. Melrose.
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In this thesis we present partial progress towards the dynamic formation of black holes in the four-dimensional Einstein vacuum equations from Christodoulou's short-pulse ansatz. We identify natural scaling in a putative solution metric and use the technique of real blowup to propose a desingularized manifold and an associated rescaled tangent bundle (which we call the "short-pulse tangent bundle") on which the putative solution remains regular. We prove the existence of a solution solving the vacuum Einstein equations formally at each boundary face of the blown-up manifold and show that for an open set of restricted short-pulse data, the formal solution exhibits curvature blowup at a hypersurface in one of the boundary hypersurfaces of the desingularized manifold. This thesis is intended to be partially expository. In particular, this thesis presents an exposition of double-null gauges and the solution of the characteristic initial value problem for the Einstein equations, as well as an exposition of a new perspective of Christodoulou's monumental result on the dynamic formation of trapped surfaces .
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020Cataloged from the official PDF of thesis.Includes bibliographical references (pages 303-305).
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Massachusetts Institute of Technology