Exotic matter and MOND as special cases of a more general solution in pure general relativity

Several solutions have been proposed to explain the dark matter (DM) component, but two explanations stand out. The most widely accepted is the assumption of the existence of exotic matter, and the second is the assumption of a modification of gravitation called MOND. We show in this article that the solutions of exotic matter and MOND are particular cases of a more general solution of pure general relativity that explains DM with only baryonic matter and without modifying gravity. Within the framework of general relativity linearization (GRL), we first demonstrate that these two explanations (exotic matter and GRL solution) are so close that all explanations within the framework of the exotic matter assumption can be translated within the GRL solution. Conversely, certain effects appear in this alternative that should not be observed in the hypothesis of exotic matter. Different types of alignments (about axes of rotation or planar trajectories) should appear on different types of objects (dwarf satellite galaxies, galaxies, or clusters of galaxies). Observational monitoring of the dynamics of S-2 stars close to our Galactic Center in the future should reveal (due to greater precision) discrepancies from the theory, explainable by the lower mass of SgrA* compensated by a stronger-than-expected GRL field (instead of exotic matter). The implementation of simulations to explain the structuring of the universe on a large scale should be able to reveal filaments or walls and large voids, thanks to a stronger-than-expected GRL field (explaining the DM component instead of exotic matter). The size of these structures would be correlated with the intensity of this GRL field. We show that this solution responds to the points addressed to all alternatives to exotic matter. Conversely, we propose points challenging the exotic matter assumption that are naturally explained in this DM component alternative explanation.