Isotropic solutions of the EinsteinLiouville equations.
Abstract
The gravitational field generated by a gas whose oneparticle 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 worldvelocity field; second, if the particles have restmass zero, the gas is irrotational. It is shown that the model is then either stationary or a RobertsonWalker model. The time dependence of the radius in the RobertsonWalker models is given in terms of integrals containing the distribution function.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 1968
 DOI:
 10.1063/1.1664720
 Bibcode:
 1968JMP.....9.1344E