Asymptotic description of the formation of black holes from short-pulse data
Name
1191266807-MIT.pdf
Size
1.86 MB
Format
Adobe PDF
Checksum (MD5)
2295779d6a8127e32cd92fd355012abe
Author(s)
Jaffe, Ethan Yale.
Advisor(s)
Richard B. Melrose.
Date Issued
2020
Publisher
Massachusetts Institute of Technology
Abstract
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 [13].
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 303-305).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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