  We consider the modification of the formulas for black hole radiation, due to
the self-gravitation of the radiation. This is done by truncating the coupled
particle-hole system to a small set of modes, that are plausibly the most
significant ones, and quantizing the reduced system. In this way we find that
the particles no longer move along geodesics, nor is the action along the rays
zero for a massless particle. The radiation is no longer thermal, but is
corrected in a definite way that we calculate. Our methods can be extended in a
straightforward manner to discuss correlations in the radiation, or between
incoming particles and the radiation.
