Unification of Newtonian Physics with Einstein Relativity Theory by using Generalized Metrics of Complex Spacetime and application to the Motions of Planets and Stars, eliminating Dark Matter

Abstract

In this paper we unify Theories of Physics (TPs) with real or infinite Universal Speed (cI), such as Einstein Relativity Theory (ERT) and Newtonian Physics (NPs). Generalized Special Relativity (SR) relates the frames of Relativistic Inertial observers (RIOs) where the spacetime has the metric gI=diag(gI00, gI11, gI11, gI11). The parameter ξI=sqrt(-gI11/gI00) is contained in the matrix (ΛI) of the Euclidean Closed Linear Transformation of complex spacetime (ECLSTT). Besides the elements of ΛI are complex numbers. So, the corresponding spacetime is necessarily complex and there exists real cI=c/ξI. In addition, the complex Cartesian Coordinates (CCs) of the theory, may be turned to the corresponding real CCs, in order to be perceived by human senses. The new real transformation is not closed (the corresponding real matrices ΛIR do not form a group) and the successive real transformations produce Generalized Thomas Rotation. The specific value ξI=1 gives Vossos transformation (VT) endowed with Lorentz metric (for gI11=1) of complex spacetime and invariant speed of light in vacuum (cI=c), which produce the Lorentzian version of Euclidean Complex Relativistic Mechanics (ECRMs). The corresponding real matrix (ΛIR) is the matrix of Lorentz Boost (ΛIR=ΛL). The specific value ξI→0 gives Galilean Transformation (GT) with invariant time, in which any other ECLSTT is reduced, if one RIO has small velocity wrt another RIO. Thus we unify TPs such as NPs and ERT, keeping the formalism of ERT. The generalized definition of Proper Time (r) gives us the possibility to compute four-velocity, four-momentum, Relativistic Doppler Shift etc, building the whole structure of the Generalized SR and General Relativity (GR). For instance the Generalized Relativistic Energy of Rest Mass (m) is Erest=mc2/ξI2. In case of NPs, the annihilation energy becomes infinite. Thus the Lomonosov-Lavoisier Law becomes clear theorem of NPs. In addition, the case of observers with variable metric of spacetime leads to GR. Thus we produce the 1st Generalized Schwarzschild metric (1GSM) and 2nd Generalized Schwarzschild metric (2GSM), which are in accordance with Einstein field equations for any TPs. In case of 1GSM, we compute the corresponding Lagrangian, geodesics, equations of motion, precession of planets’ orbits etc, resulting formulas which are referred to any TPs. We then combine the theoretical results to the experimental data of our Solar system, producing a set of valid values of ξI. In case of 2GSM, the combination of its Galilean version with Modified Newtonian Dynamics (MOND), leads to MOND relativization. After, we pass to RIOs with ordinary flat spacetime (Minkowski space), extending MOND methods to ERT. We use Simple and Standard Interpolating Function (μ) to the Lorentzian-Einsteinian version of 2GSM for the explanation of Rotation Curves in Galaxies as well as the Solar system, eliminating Dark Matter. Generally, this approach, in non rotating black hole, planetary and star system scale, coincides to the original Schwarzschild metric, while in galactic scale, it gives MONDian results. In universal scale, the gravitational field strength becomes negative, producing slight antigravity.