In this work, we study the analytical properties of the Bondi equations but assuming that the source of mass is changing in time. This Non-Stationary solution has the property of characterize better the situation in the center of galaxies where the BH is increasing in mass according to the Sigma-BH relation (Chamber etal. 2017). The stationary index goes as ~1/2. In Intergalactic medium this may implied an extra quatity of Osygen.