Vibrations of inhomogeneous non-rotating gravitational systems

Dispersion relations are obtained and analysed for a non-uniform, non-rotating gravitational system. A restriction to short wavelengths makes it possible to consider a linearized form of the collisionless Boltzmann equation, differing from that for homogeneous systems by the appearance of a term expressing the effect of the mean self-gravitational field upon the motion. The mean field affects the radially directed wave perturbations, with a breaking of symmetry. Inwardly and outwardly directed modes have quite different propagation characteristics, inward modes being preferentially propagated. Locally, the stability of the system is found to be enhanced due to the effect of the mean field. © 1975 D. Reidel Publishing Company.SCOPUS: ar.j