Spherically symmetric, self-gravitating dust is always 'self-similar'

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Abstract
This paper discusses spherically symmetric, self-gravitating dust from both the Newtonian and Einsteinian perspectives. A unified treatment in terms of comoving or Lagrangian coordinates is advocated, The most general type of self-similarity can be elucidated with this problem. It is argued that all Tolman solutions are in fact self-similar in the Lie sense in which an integral exists along a certain curve in space-time. These do not have a simple covariant expression in general at present. The limits in which more restrictive definitions apply are also explored. Finally, I treat the problem of classical spherical collapse with pressure in the same way. It is shown that previous discussions may thereby be simplified.

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