General Relativity Can Explain Dark Matter without Exotic Matter

Dark matter is one of the most important mystery in astrophysics. Several explanations have been proposed. The most accepted one is the existence of an exotic matter, exotic because unsensitive to electromagnetism, unlike baryonic matter. One problem is that except on scales beyond the galaxies, no new matter is needed. This is an ad hoc addition only for large structures of the universe. But then another problem is that this added matter that should concern large astrophysical structures is not a slight correction of the quantities of matter, but it makes the only known baryonic matter a slight correction of this exotic matter. It means that gravitation theory would have been founded on a particular matter. From this point of view, baryonic matter would finally be the exotic matter and dark matter the normal one. But despite its dominance, no new matter has been discovered to date. In this article we propose a new explanation of dark matter compliant with General Relativity and without new matter. Furthermore, MOND-based theories appear as particular solutions of this explanation and allows demonstrating the Tully-Fisher relation. The clusters of galaxies would generate an extremely light Lense-Thirring effect on galaxies in the form of a relatively uniform and very weak field.