On the critical mass of the collapse of a gaseous star in spherically symmetric and isentropic motion

For self-gravitating, spherically symmetric and isentropic gaseous star, there is a family of particular solutions when the adiabatic index γ = 4/3. We found that there is a critical total mass M0 associated with these particular solutions. If the total mass M of star less than M0, then the star expands infinitely and its density ultimately tends to approach zero. When M ≥ M0 and the initial velocity is slower than escape velocity, then the gas is trapped and collapses toward the star's center in a finite period of time.