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The idea is simple. Let's say we arrange similar bodies (call them planets, ions, anything) in an infinite crystal structure, but the only possible interactions are gravitational interactions.

A sensible guess is, the system will be unstable, it won't change unless it's perturbed, and if it is, it would not go back to the previous state after the perturbation.

Now, that was an obvious thing to guess. My question is, what else would change? What properties would disappear? Can we recover some of them?

Could we have, for example, lattice vibrations, and so on?

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  • $\begingroup$ Since vibrations are perturbations, you can have at most one of them before the whole thing collapses (and they wouldn't look like vibrations so much as a propagating destruction of the lattice). That said, was there a specific list of "properties" of crystals that you had in mind? $\endgroup$ – probably_someone Dec 13 '18 at 13:41
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    $\begingroup$ The situation is not metastable, it is unstable. A stable lattice (even a metastable one) requires a mixture of attractive an repulsive interactions to give rise to a potential minimum as a point in free space. $\endgroup$ – By Symmetry Dec 13 '18 at 13:43
  • $\begingroup$ @probably_someone I don't really have a list in mind. I have a rough idea that we can actually make the lattice vibrate if we send smaller bodies traveling between the big ones at different intervals, for example. I just want to see what other ideas arise $\endgroup$ – UriAceves Dec 13 '18 at 13:48
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    $\begingroup$ You cannot hold rigid it in place with only attractive forces. We have planetary systems, not lattices, imo. $\endgroup$ – anna v Dec 13 '18 at 14:03
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    $\begingroup$ Related: physics.stackexchange.com/q/11054/2451 , physics.stackexchange.com/q/2196/2451 and links therein. $\endgroup$ – Qmechanic Dec 13 '18 at 17:21
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Much of the behavior of a crystal is governed by thermodynamics.

The thermodynamics of purely gravitational systems are quite counterintuitive. For one example, the heat capacity of a gravitational system is negative: when you add energy, it gets cooler. (There's a proof of this in Schroeder's thermo textbook, but if you know some astronomy you already know one consequence of this: if the energy output of a star's core increases because of a change from hydrogen fusion to helium fusion, the star gets brighter but cooler. We call these "red giants.") So if you have in mind "crystals do X," you have some hard thinking to do about why X happens and whether a gravitational system would do the same sort of thing.

What makes crystals stable is an interplay between attractive and repulsive forces. In gravitational systems you have only attraction. A disordered gravitational system eventually collapses to become a star-forming region. An ordered gravitational system, without any restoring repulsive forces, would rapidly become disordered, and from there eventually collapse to become a star-forming region.

If you consider an infinite gravitationally-bound uniform-density system, you should recover big-bang cosmology.

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  • $\begingroup$ So a close-packed, gravitationally bound assembly of marbles is not possible? Treated as hard-shelled spheres, there is repulsion in addition to the attraction. It would like to be close-packed. Sure, for a star-sized system of marbles the repulsion would not last, but for a few million marbles there would not be any issues. $\endgroup$ – Jon Custer Dec 13 '18 at 14:34
  • $\begingroup$ That sounds like a "gravel pile" asteroid --- though the hard-shell repulsion is a non- gravitational interaction. $\endgroup$ – rob Dec 13 '18 at 15:38

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