Explanation of Light Deflection, Precession of Mercury’s Perihelion, Gravitational Red Shift and Rotation Curves in Galaxies, by using General Relativity or equivalent Generalized Scalar Gravitational Potential, according to Special Relativity and Newtonian Physics

Abstract

Abstract The development of Geometric theories of gravitation and the application of the Dynamics of General Relativity (GR) is the mainstream approach of gravitational field. Besides, the Generalized Special Relativity (GSR) contains the fundamental parameter (ξ I) of Theories of Physics (TPs). Thus, it expresses at the same time Newtonian Physics (NPs) for ξ I→ 0 and Special Relativity (SR) for ξ I=1. Moreover, the weak Equivalence Principle (EP) in the context of GSR, has the interpretation: m G=m, where m G and m are the gravitational mass and the inertial rest mass, respectively. In this paper, we bridge GR with GSR. This is achieved, by using a GSR-Lagrangian, which contains the corresponding GR-proper time. Thus, we obtain a new central scalar GSR-gravitational generalized potential V=V(k,l,r,r_dot,ϕ _dot), where k=k(ξ I), l=l(ξ I), r is the distance from the center of gravity and r_dot, ϕ _dot are the radial and angular velocity, respectively. The replacement k=1 and l=ξ I 2 makes the above GSR-potential equivalent to the original Schwarzschild Metric (SM). Thus, it explains the Precession of Mercury’s Perihelion (PMP), Gravitational Deflection of Light (GDL), Gravitational Red Shift (GRS) etc, by using SR and/or NPs. The procedure described in this paper can be applied to any other GR-spacetime metric, in order to find out the corresponding GSR-gravitational potential. So, we also use the GR-proper time of the 3rd Generalized Schwarzschild Metric (3GSM) and we obtain the central scalar GSR-gravitational potential V=V(a,k,l,r_dot,ϕ _dot), where a=a(r). The combination of the above with MOND interpolating functions, or distributions of Dark Matter (DM) in galaxies, provides the functions corresponding a=a(r). Thus, we obtain a new GSR-Gravitational field, which explains the PMP, GDL, GRS as well as the Rotation Curves in Galaxies, eliminating the corresponding DM.