Anisotropic solutions of the Einstein-Boltzmann equations: I. General formalism

Journal Article · Sat Oct 15 04:00:00 EDT 1983 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(83)90023-4· OSTI ID:5168644

Ellis, G F.R.; Matravers, D R; Treciokas, R

Given a choice of a timelike vector field, a particle distribution function in a general curved space-time can be analysed into spherical harmonics; the Liouville and Boltzmann equations can then be written as a set of equations relating these spherical harmonic components. We obtain these equations and the resulting equations for the spherical harmonic moments of the distribution function. An orthonormal tetrad formalism is used as an aid in our calculations; the set of moment equations used can be completed by giving Einstein's field equations as equations for the rotation coefficients of this tetrad. We discuss time and space reversal symmetry properties of the Boltzmann equation, but leave applications of the set of equations obtained to further papers.

• Research Organization: Department of Applied Mathematics, University of Cape Town, Rondebosch 7700, South Africa
• OSTI ID: 5168644
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 150:2; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

657003* -- Theoretical & Mathematical Physics-- Relativity & Gravitation
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANISOTROPY
BOLTZMANN EQUATION
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EINSTEIN FIELD EQUATIONS
ELEMENTARY PARTICLES
EQUATIONS
FIELD EQUATIONS
FIELD THEORIES
FUNCTIONS
GENERAL RELATIVITY THEORY
PARTIAL DIFFERENTIAL EQUATIONS
SPACE-TIME
SPHERICAL HARMONICS
TENSORS
VECTOR FIELDS