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Geometric analysis of the Einstein Equations

Dr. Stefan Czimek

Mittwoch, 2020-10-21 15:30Uhr

The Einstein equations of general relativity constitute a hyperbolic system of non-linear geometric partial differential equations. The equations’ non-linear geometric nature causes the formation of singularities and interesting asymptotics of solutions (e.g. black holes as final states). In this talk I will discuss how such phenomena can be tracked and controlled through the application of analysis tools (such as bilinear/trilinear estimates, sharp trace estimates, Besov spaces, Cheeger-Gromov theory and linear analysis). Specifically, I will present my research results and projects on (1) low regularity estimates for the Einstein equations (assuming the curvature to be only $L^2$-integrable) and (2) the asymptotic analysis of solutions along null hypersurfaces.