Gravitational collapse of gas clouds with spherical,cylindrical or plane symmetry in the linear wave flow approximation

The equations of gas dynamics are solved, quasi-analytically by applying McVittie's method for spherical, cylindrical and plane configurations. The hypothesis of linear wave flow is applied and it is assumed that the final state of collapsing clouds is a hydrostatic equilibrium state, determined by complete polytropes. Complete analytical solutions are found when the generalized (to the three symmetries) Emden equation admits of analytical solutions. Otherwise the solutions are left in terms of the numerical solutions of the Emden equation. Numerical solutions to the Emden equation in the plane case are found and tabulated. A strong dependence of amplification, of density, pressure and temperature of the gas, on the symmetry is found. In addition, it is conclude that the flow remains subsonic, during the collapse, except toward the boundaries of the collapsing clouds.