Against Geometry: Nonstandard General Relativity

We show that the Schwarzschild solution can be embedded in a class of nonstandard solutions of the vacuum Einstein’s equations with arbitrary rotation curves. These nonstandard solutions have to be taken as physical, if dark matter as needed in the standard theory cannot be found. As a consequence general relativity is considered as a classical field theory in Minkowski space and not as a geometric theory in the sense of Einstein. Assuming an asymptotically flat rotation curve and introducing a material disk into this model we find a matter density in accordance with the Tully- Fisher relation.