In both Newtonian gravity and General Relativity, an initially static universe with uniform dust collapses in a finite time into a singularity. In fact, Newton and GR predict the same speed of collapse and are indistinguishable for slow-moving observers.
What about an infinite dust plane? It would be like a domain wall but made out of dust instead having a $p=-2/3\rho$ tension. Would it collapse?
It does not seem to collapse under Newtonian gravity. A V-shaped $\phi = k |z|$ solves Poissons equation for an x-y plane of uniform mass/area and $k=2\pi G \rho$. Since there are no force (gradients) in the x or y direction, the plane will not collapse. I don't see a reason why it would collapse under GR.
A plane is an unstable equilibrium in Newtonian gravity in that it will tend to break up into an irregular grid of "galaxies and clusters" if perturbed. Presumably, in GR this is also the case.
In Newtonian gravity, the gravity is constant and does not decrease with distance. But I think that GR is different. Presumably the spacetime outside of the plane is flat (since Newtonian physics predicts no tidal forces). In which case the problem becomes computing accelerations in Rindler coordinates and the result is that the gravity drops off as $g = \frac {g_0} {1+|z g_0 /c^2|}$, where $z$ is (I think) the proper distance measured by static ropes. But is my assumption of flat space outside the plane correct?
