Anisotropic fluid in a spherical space-time: II. Most probable state of high-frequency null radiation
✍ Scribed by Daniel C Wilkins
- Publisher
- Elsevier Science
- Year
- 1977
- Tongue
- English
- Weight
- 907 KB
- Volume
- 109
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
An infinite system of coupled differential equations govern the free propagation in a spherical space-time of a gas of massless particles. Following the information-theoretic ideas of E. T. Jaynes, the entropy of the gas is maximized for given energy density, speed, etc., to determine the most probable state of the gas. Assuming this state, the transport equations reduce to a small closed system which is the same for Bosons, Fermions, and distinguishable particles. Because the gas is collisionless, it will usually be nonisotropic, having different pressures in the radial and transverse directions. We assume one restriction motivated by the statistical method and also that the anisotropy measured by the ratio of radial pressure to energy density (equal to 4 for the isotropic case) is a time-independent function of comoving position. This enables one to solve exactly the combined system of general relativistic plus transport equations. The general solution is a homogeneous, isotropic Tolman universe filled with massless quanta.