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Continuation of solutions of Einstein’s equations

CMSA EVENTS: CMSA GENERAL RELATIVITY SEMINAR

When: October 8, 2024
11:00 am - 12:00 pm
Where: CMSA, 20 Garden St, G10
Address: 20 Garden Street, Cambridge, MA 02138, United States
Speaker: Oswaldo Vazquez (Northeastern University)
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.
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Zoom: https://harvard.zoom.us/j/7855806609