Two linearization procedures for the Boltzmann equation in ak=0 Robertson-Walker space-time |
| |
Authors: | Zbigniew Banach Sławomir Piekarski |
| |
Affiliation: | (1) Center of Mechanics, Institute of Fundamental, Technological Research, Department of Fluid Mechanics, Polish Academy of Sciences, 00-049 Warsaw, Poland;(2) Institute of Fundamental Technological Research, Department of Theory of Continuous Media, Polish Academy of Sciences, 00-049 Warsaw, Poland |
| |
Abstract: | It is the aim of this paper to describe two different linearization procedures for the Boltzmann equation in ak=0 Robertson-Walker space-time. These procedures are discussed with a view to obtaining an asymptotic form of the Boltzmann equation for the late stages of cosmic expansion where the behavior appropriate to a nonrelativistic gas is encountered. Using the asymptotic kinetic equations, a necessary and sufficient condition is formulated under which every small perturbation of the equilibrium distribution function, either classical or relativistic, decays to zero as time goes on. The same condition can be extracted from each of two linearization procedures, and in this sense a comparison is made of these approaches which reveals mutual agreement. Also, applying an asymptotic theory of the Einstein-Boltzmann system, we show that the final state of a gas is dust (i.e., a fluid with zero temperature and pressure). Comparison with the predictions of the Eckart fluid model is briefly presented. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|