  We use the post Newtonian (pn) order of Liouville's equation (pnl) to study
the normal modes of oscillation of a relativistic system. In addition to
classical modes, we are able to isolate a new class of oscillations that arise
from perturbations of the space-time metric. In the first pn order; a) their
frequency is an order q smaller than the classical frequencies, where q is a pn
expansion parameter; b) they are not damped, for there is no gravitational wave
radiation in this order; c) they are not coupled with the classical modes in q
order; d) in a spherically symmetric system, they are designated by a pair of
angular momentum eigennumbers, (j,m), of a pair of phase space angular momentum
operators (J^2,J_z). Hydrodynamical behavior of these new modes is also
investigated; a) they do not disturb the equilibrium of the classical fluid; b)
they generate macroscopic toroidal motions that in classical case would be
neutral; c) they give rise to an oscillatory g_{0i} component of the metric
tensor that otherwise is zero for the unperturbed system. The conventional
classical model are, of course, perturbed to order q. These, however, have not
been discussed in this paper.
