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DTSTART;TZID=America/New_York:20241008T110000
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DTSTAMP:20260501T203822
CREATED:20240903T181702Z
LAST-MODIFIED:20241004T144050Z
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SUMMARY:Continuation of solutions of Einstein's equations
DESCRIPTION:General Relativity Seminar \nSpeaker: Oswaldo Vazquez\, Northeastern University \nTitle: Continuation of solutions of Einstein’s equations \nAbstract: Klainerman-Rodnianski improved the continuation criterion for the solutions of Einstein’s equations proved by Michael Anderson using Kirchoff-Sobolev type parametrix and geometric Littlewood-Paley theory. Using their technique but a new parametrix we prove a continuation condition in the context of 3+1 dimensional vacuum Einstein gravity in Constant Mean extrinsic Curvature (CMC) gauge. More precisely\, we obtain quantitative criteria under which the physical spacetime can be extended indefinitely in the future as a solution to the Cauchy problem of the Einstein equations given regular initial data. In particular\, we show that a gauge-invariant H^2 Sobolev norm of the spacetime Riemann curvature remains bounded in the future time direction provided the so-called deformation tensor of the unit timelike vector field normal to the chosen CMC hypersurfaces verifies a spacetime L^{\infty} bound.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-seminar-10824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
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