Isotropic solutions of the Einstein-Liouville equations.
Abstract
The gravitational field generated 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.
- Publication:
-
Journal of Mathematical Physics
- Pub Date:
- 1968
- DOI:
- 10.1063/1.1664720
- Bibcode:
- 1968JMP.....9.1344E