  A hydrodynamic model for small acoustic oscillations in a cloud of stars is
built, taking into account the self-consistent gravitational field in
equilibrium with a non-zero second correlation moment. It is assumed that the
momentum flux density tensor should include the analog of the anisotropic
pressure tensor and the second correlation moment of both longitudinal and
transverse gravitational field strength. The non-relativistic temporal equation
for the second correlation moment of the gravitational field strength is
derived from the Einstein equations using the first-order post-Newtonian
approximation. One longitudinal and two transverse branches of acoustic
oscillations are found in a homogeneous and isotropic star cloud. The
requirement for the velocity of transverse oscillations to be zero provides the
boundary condition for the stability of the cloud. The critical radius of the
spherical cloud of stars is obtained, which is precisely consistent with the
virial theorem.
