New Central Scalar Gravitational Potential according to Special Relativity and Newtonian Physics, explains the Precession of Mercury’s Perihelion, the Gravitational Red Shift and the Rotation Curves in Galaxies, eliminating Dark Matter

Abstract

The mainstream approach of gravitational field is the development of Geometric theories of gravitation and the application of the Dynamics of General Relativity (GR). Besides, the Generalized Special Relativity (GSR) contains the fundamental parameter (ξI) of Theories of Physics (TPs). Thus, it expresses at the same time Newtonian Physics (NPs) for ξI→0 and Einstein Relativity Theory (ERT) for ξI=1. Moreover, the Equivalence Principle (EP) in the context of GSR, has two possible interpretations: mG = m (1), or mG=γ(ξI,β)m (2), where β=υ/c and mG, m, γ are the gravitational mass, inertial rest mass and Lorentz γ-factor, respectively. In this paper we initially present a new central scalar potential V=V(k,r), where k=k(ξI) and r is the distance from the center of gravity. We demand that ‘this new GSR gravitational field in accordance with EP (1), gives the same precession of Mercury’s orbit as Schwarzschild Metric (SM) does’ and we obtain k=6-ξI2. This emerges Einsteinian SR-horizon at r=5rS, while NPs extends the horizon at six Schwarzschild radius (6rS).We can also explain the Gravitational Red Shift (GRS), if only the proposed GSR Gravitational field strength g=g(k,r) is combined with EP (2). We modify the aforementioned central scalar potential as V=V(h,k,r), where h=h(r). The combination of the above with MOND interpolating functions, or distributions of Dark Matter (DM) in galaxies, provides six different functions h=h(r). Thus, we obtain a new GSR central Gravitational field strength g=g(h,k,r), which not only explains the Precession of Mercury’s Perihelion, but also the Rotation Curves in Galaxies, eliminating Dark Matter.