Density waves in gravitationally interacting particles

[ohad]

My question is about system of infinite number of point like particles with gravitation interaction (classic Newtonian interactions).
If the infinite system can be considered to be in equilibrium, uniform density, in 3D, did anyone analyzed this system with regard to propagation of density waves?
If so, what is the waves velocity and are they sustainable?

I read few chapters from Chandrasekhar's books and I tried to search for articles about it.
one article even stated that this issue was not yet solved in 3d:
http://www.if.ufrgs.br/~levin/Pdfs.dir/gravity1d.pdf
(Statistical mechanics of 1D self-gravitating systems: the core–halo distribution)

I know this issue was investigated very carefully in context of spiral galaxies, but it was not general to infinite configuration.

I really appreciate any help you can give me

 

[vanhees71]

The kinetics of gravitational systems is tricky, because of the long-range nature of the gravitational potential. Usually you find a chapter about the non-relativistic (i.e., non-GR) situation in many cosmology textbooks when it comes to structure formation.

 

[ohad]

I looked around for this issue a while ago and the problem with cosmology treatment of this issue is that the timescales of close encounters is very large in relation to the evolution time. When such limitation is imposed, it means that waves are propagated dispersively.
I remember that I encountered somewhere (but I don't remember exactly where) in a claim that if close encounter timescale is very short in regard to the evolution time, waves are propagated non-dispersively.
My questions are:
1. Do you know about an analysis of non-dispersive waves propagation in such a medium?
2. Can transverse waves exist in such a medium (in ideal gas it cannot)?

Any hint will be of great help.