The critical mass of compressible viscous gas-stars

Abstract

Let gamma be the adiabatic index of self-gravitating, spherically symmetric motion of compressible viscous gas-star. When gamma is an element of (1, 2], we prove the existence of nonisentropic equilibrium. Furthermore, at the adiabatic index gamma = 4/3, we found a family of particular solutions which corresponds to an expansive (contractive) gaseous star. Moreover, we find that there is a critical total mass M-0. If the total mass M of star is less than M-0, then the star expands infinitely. However, if M greater than or equal to M-0, then there is an "escape velocity" v(e)r associated with M and the initial configuration of the star. If v(0, r) 2 v(e)r, then the star will expand infinitely. If v(0, r) greater than or equal to v(e)r, then it will collapse after a finite time.