A non-Euclidean Newtonian limit of General Relativity скачать в хорошем качестве

A non-Euclidean Newtonian limit of General Relativity

Quentin Vigneron (CRAL, Lyon, France) I will be interested in defining a limit from general relativity, called non-Euclidean Newtonian limit, leading to a theory which is locally equivalent to Newtonian gravitation, but with a non-Euclidean geometry. It is constructed using the geometrised limit of Dautcourt, Künzle and Ehlers, corresponding to a limit from a Lorentzian manifold, carrying solutions of the Einstein equations, to a Galilean manifold. For non-Euclidean spatial geometries to be allowed in this limit, the stress-energy tensor in general relativity needs to feature additional source terms linked to the spatial Ricci curvature, especially an 'energy curvature' and 'anisotropic stress curvature'. We discuss the relevance of these terms for relativistic cosmology.