The Mathematical Origin of Gravitational Singularities

Abstract

In this note we give a geometrical presentation to the 4D Riemannian curvature as it relates to the Newtonian gravity in the 4D Lorentz manifold. The compacting of the proper time as is necessary for the unification with the Maxwell electrodynamics, as given by Einstein and Kaluza-Klein, should the universe be only of 4D space-time, led to the concept of gravitational field singularity sinks known as black holes, that would not be acceptable under a 5D homogeneous manifold through which the 4D Lorentz manifold evolved by application of the Perelman-Ricci Flow entropy mapping, which is consistent with both Maxwell suggested magnetic monopole, the quantum Higgs vacuum theory and the Gell-Mann standard model for hadrons.