Generalized Gauss's Law of Gravity with off-Spherical Symmetry Transition of Gravitational Field Flux Distribution

A gravitational field flux conservation and redistribution picture is proposed by generalizing the Integral Gauss's law of gravity at non-relativistic limit. 1/r dependence along with a disk thickness dependence of gravitational field and the flat rotation curves are obtained by a Gaussian surface with cylindrical symmetry, where most of the gravitational fluxes are assumed to be distributed eventually along the disk plane. For disk galaxies, a spherical to cylindrical transition, across a critical field strength, of the Gaussian surface symmetry is shown to give directly the algebraic M ∝ v⁴ baryonic Tully-Fisher relation. The Faber-Jackson relation of the elliptical galaxies can also be shown by a similar off-spherical symmetry transition for the flux distribution. The transition suggests that the 10^-10 m/s² acceleration scale can be alternatively interpreted as a critical field strength where gravitational flux redistribution occurs. The generalized Gauss's law of gravity is compared with the theoretical MOND Lagrangian modeling. One benefit of this non-dark matter field flux re-distribution picture with asymmetrically focused field lines is apparently the feasibility of extension to even larger scales where the current MOND modeling appears to be still short of mass. This gravitational flux redistribution picture may create the need for a non-Newtonian non-relativistic limit for the General Relativity. The possible applications of the temporal evolution of the "cylindrical to spherical transition" from the gravitational field flux re-distribution mechanism is also discussed.