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

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