| Hawking's discovery that a black hole quantum mechanically radiates energy like a black body suggests that its mass should decrease, leading to a process known as black hole evaporation. Solving for the evaporating black hole geometry (that is, its metric) exactly doesn't seem possible because it involves many complications. The most serious complication is that we do not have an analytic functional form for the quantum stress energy tensor in terms of the unknown metric. One approach to solving this problem is to use a Quasi-static approximation, which assumes that the evaporating black hole at every instant can be approximated by a stationary black hole. Effectively, it assumes that the luminosity of the black hole at any instant goes as 1/M^2, where M is the mass of the black hole at that instant. In this talk, I shall examine the validity of this approximation in the context of a simple model where exact numerical calculations can be performed. In this model, we assume an analytic form for the quantum stress energy tensor in terms of the unknown metric. This model is a four dimensional extension of the two dimensional black hole geometry originally investigated by Unruh, Fulling and Davies. At the end, I shall explicitly compare the results obtained from the quasi-static approximation and the exact numerical calculation performed in this model. We will observe that there is a significant difference between the quasi-static approximation and the exact calculation whenever the quantum effects are large. When the quantum effects are very small, as in astrophysical black holes, the quasi-static approximation matches the exact calculations very closely. |