Nonlinear distributional geometry and Colombeau analysis of gravitation singularities in distributional general relativity with distributional Levi-Civit‘a connection
Israel Institute of Technology, Haifa, Israel, math, Israel
Abstract: It seemed natural to identify gravitation singularities with singular values of the metric or curvature components and their scalar combinations . However, under formal and mathematically abnormal calculation which known from a very old physics
handbooks -, such a notion depends on choosing a reference frame and includes fictious singularities which being real for some observers are absent for others.In a nutshell, there is a widespread belief that there exist true physical singularities and
unphysical,i.e.,coordinate singularities. We try to base our approach to the problem of the gravitation singularities on the fact that a gravitation singularity leads by a natural way, directly to a singularity of a space-time structure in sense of Colombeau distributional
geometry -.We aim to describe gravitation singularities using mathematically rigorous approach via Colombeau nonlinear distributional space-time structures with distributional Levi-Civit‘a connection.We pointed out that some important physical
singularities which many years mistakenly considered as coordinate singularities. -
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