  There are some approaches, either based on General Relativity (GR) or
modified gravity, that use galaxy rotation curves to derive the matter density
of the corresponding galaxy, and this procedure would either indicate a partial
or a complete elimination of dark matter in galaxies. Here we review these
approaches, clarify the difficulties on this inverted procedure, present a
method for evaluating them, and use it to test two specific approaches that are
based on GR: the Cooperstock-Tieu (CT) and the Balasin-Grumiller (BG)
approaches. Using this new method, we find that neither of the tested
approaches can satisfactorily fit the observational data without dark matter.
The CT approach results can be significantly improved if some dark matter is
considered, while for the BG approach no usual dark matter halo can improve its
results.

Astrophysics of Galaxies;General Relativity and Quantum Cosmology