  In the frame of Hamilton-Jacobi method, the back-reactions of the radiating
particles together with the total entropy change of the whole system are
investigated. The emission probability from this process is found to be
equivalent to the null geodesic method. However its physical picture is more
clear: the negative energy one of a virtual particle pair is absorbed by the
black hole, resulting in the temperature, electric potential and angular
velocity increase; then the black hole amount of heat, electric charge and
angular momentum can spontaneously transfer to the positive energy particle;
when obtaining enough energy, it can escape away to infinity, visible to
distant observers. And this method can be applied to any sort of horizons and
particles without a specific choice of (regular-across-the-horizon)
coordinates.
