  The second post-Newtonian hydrodynamic equations are analyzed within the
framework of a plane wave solution. The hydrodynamic equations for the mass and
momentum density are coupled with six Poisson equations for the Newtonian and
post-Newtonian gravitational potentials. Perturbations of the basic fields and
gravitational potentials from a background state by assuming plane wave
representations lead to a dispersion relation where the Jeans instability
condition emerges. The influence of the first and second post-Newtonian
approximations on the Jeans mass is determined. It was shown that the relative
difference of the first post-Newtonian and the Newtonian Jeans masses is
negative while the one of the second post-Newtonian approximation is positive.
The two contributions imply a smaller mass needed for an overdensity to
initiate the gravitational collapse than the one given by the Newtonian theory.
