  In this paper, a natural generalization of KMY model is proposed for the
evaporation of charged black holes. Within the proposed model, the back
reaction of Hawking radiation is considered. More specifically, we consider the
equation $G_{\mu\nu} = 8\pi \langle T_{\mu\nu}\rangle$, in which the matter
content $\langle T_{\mu\nu}\rangle$ is assumed spherically symmetric. With this
equation of motion, the asymptotic behavior of the model is analyzed. Two kinds
of matter contents are taken into consideration in this paper. In the first
case (the thin-shell model), the infalling matter is simulated by a null-like
charged sphere collapsing into its center. In the second case, we consider a
continuous distribution of spherical symmetric infalling null-like charged
matter. It is simulated by taking the continuous limit of many co-centric
spheres collapsing into the center. We find that in the thin-shell case, an
event horizon forms and the shell passes through the horizon before becoming
extremal, provided that it is not initially near-extremal. In the case of
continuous matter distribution, we consider explicitly an extremal center
covered by neutral infalling matter and find that the event horizon also forms.
The black hole itself will become near-extremal eventually, leaving possibly a
non-electromagnetic energy residue less than the order of
$\ell_{p}^{4}/e_{0}^{3}$. The details of the behavior of these models are
explicitly worked out in this paper.
