I am trying to understand the effects of gravity in the Cosmos without complications of Dark Matter/Dark energy issues. So my question is, assuming that a galaxy (for example, the Milky Way) does not contain any dark matter, does anyone know the equation that would explain how long it would take for the galaxy to collapse into the massive black hole standing in the center?
If we were to extend the question to the Universe, would the equations be different and why? (again no dark energy or $\Lambda$ or a Hubble Constant would be involved so that I can easily get my head around the question of gravity at a very large scale).
I've been trying to get information on this issue for a while, so any help with equations will be welcome. I will also appreciate some good references especially a good book on the subject.