Isotropic Solutions of the Einstein-Liouville Equations

Ehlers, Jürgen; Geren, P.; Sachs, Rainer K.

doi:10.1063/1.1664720

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Isotropic Solutions of the Einstein-Liouville Equations

MPS-Authors

Ehlers, Jürgen
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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引用

Ehlers, J., Geren, P., & Sachs, R. K. (1968). Isotropic Solutions of the Einstein-Liouville Equations. Journal of Mathematical Physics, 9(9), 1344-1349. doi:10.1063/1.1664720.

引用: https://hdl.handle.net/11858/00-001M-0000-0013-5EFE-8

要旨

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.