Determinations of the rotation speed of stars in galaxies (galactic rotation curves) based on the assumption that Newtonian gravity is a good approximation have led to the inference that a large amount of dark matter must be present - more than can be accounted for by non-luminous baryonic matter. While there are plenty of attractive theoretical candidates for the additional dark matter, such as a lightest supersymmetric particle (LSP), it is also interesting to look into the details of the calculations that suggest the need for such exotica. Now F I Cooperstock and S Tieu of the University of Victoria have reworked the problem using general relativity in place of Newtonian gravity, and they find no need to assume the existence of a halo of exotic dark matter to fit the observed rotation curves.

This is because even for weak fields and slow speeds, well-known nonlinearities change the character of the solution dramatically. The success of Newtonian mechanics in situations like our solar system can be traced to the fact that in this case the planets are basically "test particles", which do not contribute significantly to the overall field. However, in a galaxy this approximation is not a good one - all the rotating matter is also the source of the gravitational field in which everything rotates.

Further reading

F I Cooperstock and S Tieu 2005 http://xxx.lanl.gov/abs/astro-ph/0507619..