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Collision-free gases in Bianchi space-times

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Abstract

We study collision-free gases in Bianchi space-times. Spatially homogeneous distribution functions are found for all Bianchi types by supposing that the distribution functionf(x, p) is a function of the Killing vector constants of the motion only. Bianchi types I, VIII and IX only, lead to physical distributions. In types VIII and IX the average behaviour of the gas is that of a nonrotating viscous fluid. In an attempt to obtain physical spatially homogeneous distribution functions for all Bianchi types, we write the Liouville equation in a spatially homogeneous orthonormal tetrad. Furthermore, the general inhomogeneous solution of Liouville's equation in Bianchi type I is obtained, depending on constants of the motion that generalise the conserved quantities generated by Lorentz boosts in flat space-time.

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Authors and Affiliations

  1. Centre for Nonlinear Studies and Department of Computational and Applied Mathematics, University of the Witwatersrand, P. O. Wits 2050, Johannesburg, South Africa

    R. Maartens

  2. Department of Mathematics and Applied Mathematics, University of Natal, King George V Avenue, 4001, Durban, South Africa

    S. D. Maharaj

Authors
  1. R. Maartens
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  2. S. D. Maharaj
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Maartens, R., Maharaj, S.D. Collision-free gases in Bianchi space-times. Gen Relat Gravit 22, 595–607 (1990). https://doi.org/10.1007/BF00755980

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