Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
A geometric choice of asymptotically Euclidean coordinates via STCMC-foliations
Asymptotically Euclidean initial data sets (IDS) in General Relativity model instants in time for isolated systems. In this talk, we show that an IDS is asymptotically Euclidean if it admits a cover by closed hypersurfaces of constant spacetime mean curvature (STCMC), provided these hypersurfaces satisfy certain geometric estimates, some weak foliation properties, and each surface exhibits generalized stability. Building on the work of Cederbaum and Sakovich (2021), which established that every asymptotically Euclidean IDS has a unique STCMC foliation, we conclude that the existence of such a foliation characterizes asymptotically Euclidean IDS. Furthermore, we explore the connections to the center of mass and show why these coordinates seem well-adapted to describe this concept. This is joint work with O. Vičánek Martínez.
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