General relativistic galaxy models.

In 2006 Cooperstock and Tieu suggested that the spherical dark matter halos used to successfully model the rotation curves of spiral galaxies with Newtonian dynamics are not required. Instead, one can use rotating dust solutions purely in general relativity. This work is controversial and various technical points are disputed. The follow-up paper by Balasin and Grumiller, which comes to similar conclusions, also has some technical flaws. In this project we investigate, with a view to potentially improve, these results. We find that Cooperstock and Tieu's model does not give physically reasonable behaviour at spatial infinity in the radial direction. Additionally, we find that the particular solution of Cooperstock and Tieu is not consistent with a prescribed empirical density pro le, even though we show that the general system of equations is. We also find that the boundary conditions imposed to obtain Balasin and Grumiller's solution are unsuitable, as these were set in regions which are not physically admissible. Moreover, we discover contradictions arising from the separation ansatz used in both papers, suggesting that one must instead solve the system of equations more generally, with care taken to set physically reasonable boundary conditions. Towards this end we have obtained a first order partial differential equation from the system of equations which may be solved in future work. While the general relativistic approach may not eliminate the need for nonbaryonic darkmatter, it might produce a different value of the dark matter-to-baryon ratio which may be signi ficant in discriminating between different cosmological models