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Suppose we have a uniform-density spherical cloud of gravitating dust (i.e., zero-pressure matter with negligible non-gravitational interactions) at non-zero temperature. Within such a sphere, the gravitational force rises proportional to radius, before converting to a typical inverse-square fall-off on the exterior. Because the cloud has zero pressure, however, it won't remain that way--particles will collapse towards the center, changing the density profile and invalidating the trivial solution that gives a radius-proportional force law.

Once such a cloud comes to equilibrium, what does the internal gravitational field look like?

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