We derive the metric for a simple class of isothermal inhomogeneous universes in which the nonzero pressure balances gravity. These models are spherical and static. There exists a family of such models in which the isothermal universe is a special case. These models may represent the ultimate state of an Einstein-de Sitter universe that undergoes a phase transition caused by gravitational clustering.
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Saslaw et al. (1996) studied this question.
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