Isotropic Solutions of the Einstein-Liouville Equations

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Abstract
The gravitational fieldgenerated by a gas whose one‐particle distribution function obeys the Liouville equation is examined under the following assumptions: First, the distribution is locally isotropic in momentum space with respect to some world‐velocity field; second, if the particles have rest‐mass zero, the gas is irrotational. It is shown that the model is then either stationary or a Robertson‐Walker model. The time dependence of the radius in the Robertson‐Walker models is given in terms of integrals containing the distribution function.

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