An idealized $\infty$-body problem: is an infinite and regular configuration of massive objects stable?

by Sofie Verbeek   Last Updated July 12, 2019 09:20 AM - source

Suppose I have an infinite amount of massive point shaped objects, and I arrange the objects by putting one object on each point of $\mathbb{Z}^2$ within $\mathbb{R}^2$. By symmetry, the gravity exerted on every object should add up to zero, so that nothing should happen to the system. Now suppose that I slightly perturb one of the objects. Will the resulting system collapse or will it stabilise?

There are obvious generalisations involving either higher dimensions or other kinds of regular configurations, and I'd be happy to hear more about that too, but for now let's restrict to the simplest situation stated above. Also, feel free to alter the tags, as I wasn't sure where to put this.

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