Plane wave analysis of the second post-Newtonian hydrodynamic equations

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