March 02, 2006

General Relativity and Galactic Distances

My colleague T. Perko informed me of a paper by H. Balasin and D. Grumiller titled Significant reduction of galactic dark matter by general relativity.  The authors model the matter content of a galaxy by a pressureless perfect fluid. Stationarity and axial symmetry are also imposed on the solutions of Einstein equations. Using some simplifications they solve the linear partial differential equations and conclude that the Newtonian approximation over-estimates the amount of matter in a galaxy by about a third. GR reduces the amount of dark matter needed to explain the flat rotation curves.

An earlier paper by F. I. Cooperstock and S. Tieu, titled General Relativity Resolves Galactic Rotation Without Exotic Dark Matter, makes a stronger claim of the dark matter needed in galaxies. Using a similar perfect fluid model they end up to one linear and one non-linear equation relating the angular velocity to the fluid density. From their calculation the authors conclude that the need for a massive halo of exotic dark matter is removed.

We most likely will see other studies of general relativistic galactic systems, and new estimates of the amount of dark matter in the universe. For the present, we tend consider the latter paper's conclusion somewhat striking.