Null points between galaxies

Lagrange's calculation is based on very general (but also very specialized) mathematics, in particular the Newtonian two body problem. So yes, there should be the same old 5 lagrangian points for the Milky Way and the Andromeda galaxy, since they are a reasonably good approximation to a two body system. Similarly for any other more or less isolated binary galaxies. Also true at even larger scales if you can find binary galaxy clusters or even bound binary superclusters. (I'm not aware of any, but that doesn't mean they don't exist.) Probably even more similar points exist in three and more body systems, but this is much more complex mathematics and I am not aware of any general results.
Best, Jim

 

Lagrange points rely on two assumptions. The first is that the bodies are point particles or spherical, since the external gravitational field of a spherical object is the same as the field or a point particle of the same mass. The second is that the objects are in orbit around a common centre of mass.

The first probably dosn't apply to these galaxies, and the second doesn't either. They are on a collision course rather than an orbit. If you look at the main image inhttp://en.wikipedia.org/wiki/Lagrange_points" [Broken] link you will see that Lagrange points 2-5 really on the fact that the bodies are in circular motion around the common centre of mass. This dosn't apply in this case. Lagrange point 1 may exist, however since the galaxies are not points or spheres it probably will not be a point be more of an extended region of low potential, rather than a definite trough.