pleasedInstead of using Newton's theory of gravity to examine why fast-moving stars remain within their galaxies, the pair applied general relativity, Einstein's theory of gravity, to the problem. Einstein's theory holds that matter and energy distort space, and massive bodies such as planets and stars travel in this warped space. The theory supersedes Newton's law in situations where gravity is very strong, such as next to a black hole, or where energies and speeds are very high. But neither applies to the case of stars orbiting the outer reaches of a galaxy.
The key, Dr Cooperstock claims, is a “non-linearity” that arises in Einstein's theory. If one body is much larger than its neighbours, such as the sun compared with the planets of the solar system, its effect dominates the others. But when all the bodies are very massive, such as stars in a galaxy, this non-linearity becomes important. Each star strongly influences—and is influenced by—the rest.
To their surprise, when he and Mr Tieu did the calculation with general relativity, they found that they were able to reproduce the observed speeds at which individual stars are orbiting the centre of a galaxy, without requiring the galaxy to contain dark matter. Indeed, the distribution of mass through the galaxy roughly followed the distributions of visible matter, with no need for exotic new particles.
You should know that although I, unfortunately, am not a cosmologist by any means, this theory does sound to me so brilliant as to be quite plausibly correct. Something so simple and yet so brilliant almost has to be correct. As it stands, I definitely look forwards to this hypothesis' testing.
UPDATE (9:09 AM) : A commenter links to this posting critical of Cooperstock and Tieu's paper.