Author(s)

Kai Wai Wong¹, Wan Ki Chow²

¹Department of Physics and Astronomy, University of Kansas, Lawrence, USA.
²Department of Building Services Engineering, The Hong Kong Polytechnic University, Hong Kong, China.

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.

Black Hole, Gravitational Field Singularities Within a Lorentz Manifold, Proper Time Compacting, Perelman Mappings as It Relates to Riemannian Curvature

Wong, K. and Chow, W. (2020) The Mathematical Origin of Gravitational Singularities. Journal of Modern Physics, 11, 1911-1917. doi: 10.4236/jmp.2020.1112119.