## Abstract

The kinematical and dynamical properties of one-component collision-free gases in spatially homogeneous, locally rotationally symmetric (LRS) space-times are analyzed. Following Ray and Zimmerman [Nuovo Cimento B 42, 183 (1977)], it is assumed that the distribution function f of the gas inherits the symmetry of space-time, in order to construct solutions of Liouville's equation. The redundancy of their further assumption that f be based on Killing vector constants of the motion is shown. The Ray and Zimmerman results for Kantowski-Sachs space-time are extended to all spatially homogeneous LRS space-times. It is shown that in all these space-times the kinematic average four-velocity u^{i} can be tilted relative to the homogeneous hypersurfaces. This differs from the perfect fluid case, in which only one space-time admits tilted u^{i}, as shown by King and Ellis [Commun. Math. Phys. 31, 209 (1973)]. As a consequence, it is shown that all space-times admit nonzero acceleration and heat flow, while a subclass admits nonzero vorticity. The stress π_{ij} is proportional to the shear σ_{ij} by virtue of the invariance of the distribution function. The evolution of tilt and the existence of perfect fluid solutions are also discussed.

Original language | English |
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Pages (from-to) | 2869-2880 |

Number of pages | 12 |

Journal | Journal of Mathematical Physics |

Volume | 26 |

Issue number | 11 |

DOIs | |

Publication status | Published - 1 Jan 1985 |