By solving the semi-classical Einstein equation to get a self-consistent evolution process for black holes, the earlier work of Kawai, Matsuo and Yokokura introduced the notion of a black hole where there is no horizon. In this thesis, we use both numerical simulation and analytic expression to probe the possibility of other solutions to the semi-classical Einstein equation. We find that there are two types of solutions corresponding to different initial conditions. Whenever the initial energy density of the collapsing matter is smaller than a critical value, we arrive at an asymptotic black hole. We also derive the analytic expression for the second kind of black hole. They appear when the initial energy density is higher than the critical value, and they will be called pseudo thin shells.