dc.contributor.advisor | Richard B. Melrose. | en_US |
dc.contributor.author | Jaffe, Ethan Yale. | en_US |
dc.contributor.other | Massachusetts Institute of Technology. Department of Mathematics. | en_US |
dc.date.accessioned | 2020-09-03T16:40:55Z | |
dc.date.available | 2020-09-03T16:40:55Z | |
dc.date.copyright | 2020 | en_US |
dc.date.issued | 2020 | en_US |
dc.identifier.uri | https://hdl.handle.net/1721.1/126925 | |
dc.description | Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, May, 2020 | en_US |
dc.description | Cataloged from the official PDF of thesis. | en_US |
dc.description | Includes bibliographical references (pages 303-305). | en_US |
dc.description.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]. | en_US |
dc.description.statementofresponsibility | by Ethan Yale Jaffe. | en_US |
dc.format.extent | 305 pages | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Massachusetts Institute of Technology | en_US |
dc.rights | MIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided. | en_US |
dc.rights.uri | http://dspace.mit.edu/handle/1721.1/7582 | en_US |
dc.subject | Mathematics. | en_US |
dc.title | Asymptotic description of the formation of black holes from short-pulse data | en_US |
dc.type | Thesis | en_US |
dc.description.degree | Ph. D. | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Mathematics | en_US |
dc.identifier.oclc | 1191266807 | en_US |
dc.description.collection | Ph.D. Massachusetts Institute of Technology, Department of Mathematics | en_US |
dspace.imported | 2020-09-03T16:40:55Z | en_US |
mit.thesis.degree | Doctoral | en_US |
mit.thesis.department | Math | en_US |