TheLocally Isotropic Solutions of the Liouville and Poisson Equations
Abstract
The general solution (~,f) of the Liouville equation for a collisionless system of gravitationally inter acting particles in which the distribution function f is locally isotropic in momentum space is derived. The distribution function is shown to be a spherical distribution in Chandrasekhar's sense. In the non stationary case, Poisson's equation is solved and is seen to imply a spatially constant density. The stellar orbits are determined, and a class of anisotropic distribution functions which are also compatible with the previously established potential ~ is constructed. The relation of these solutions to Newtonian cosmology is pointed out
 Publication:

The Astrophysical Journal
 Pub Date:
 January 1969
 DOI:
 10.1086/149852
 Bibcode:
 1969ApJ...155..105E