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.
Cite this paper
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