Prof. Bernd Ammann und Mitarbeiter, Zimmer 119

Christopher Nerz

Construction of canonical, asymptotically Euclidean coordinates

In mathematical general relativity, one often assumes that the space-time is foliated by space-like hypersurfaces such that each of these surfaces satisfies certain asymptotic assumptions. The latter are often defined using coordinates. For example, isolated gravitational systems are modeled by space-times which are foliated by 'asymptotically Euclidean manifolds', i. e. it is assumed that each leaf M possesses a coordinate system x mapping M (outside some compact set) to the Euclidean space (outside some ball). This means that a physical property is modeled using a non-geometric property which seems to be counterintuitive. We will resolve this by constructing 'geometric coordinate systems' using 'geometric spheres'. In this talk, we explain this for asymptotically Euclidean and spheres of constant mean curvature (CMC).
Bernd Ammann, 11.12.2015 oder später