The Effect of the (2+1)-Dimensional Gravity in the Spiral Galaxy

The slowly decreasing rotational velocity of the Milky Way suggests the existence of the dark matter. One finds that the effect of the dark matter in a galaxy can be described by a $(2+1)$-dimensional fluid model. The stability analysis for the corresponding fluid model is discussed in details in this paper. It is found that the pressure term plays an important role in the stability of the spiral arms and counteracts the increasing mass of the observed galaxy as the radial distance increases. When the fluid region ends, the $ nearly $ constant rotational velocity of the distant stars require no additional mass if the spatial dimension in the remote region is close to two. This indicates that the galaxies, we are interested, could be explained by a $(2+1)$-dimensional model. Possible implications are also discussed in this paper.