Explanation of Rotation Curves in Galaxies by Generalization of the Schwarzschild Metric and Combination with MOND-Type Theories Eliminating Dark Matter

摘要

Modified Newtonian Dynamics (MOND) has already explained the rotation curves in many galaxies, by using suitable interpolating function (μ) in Milgrom's Law. In this paper, we initially introduce the 1~(st) Generalized Schwarzschild potential, which is in accordance with any specific Theory of Physics (TPs) where the Inertial Observers (IOs) are moved in isotropic spacetime ('flat' spacetime). Modifying the above potential, we produce the 2~(nd) Generalized Schwarzschild Potential (2GSP) which describes the gravitational interaction at any distance and for any TPs. We combine 2GSP with MOND, achieving MOND relativization and we then pass to the case of Minkowski space, extending MOND methods to Einstein Relativity Theory (ERT). We use μ to the Lorentzian-Einsteinian 2GSP for the explanation of the Rotation Curves in Galaxies, eliminating the corresponding Dark Matter. The relativistic potential and the corresponding metric of spacetime have been obtained by the light of Euclidean Closed Linear Transformations of Complex Spacetime endowed with the Corresponding Metrics.