BLACK-HOLE RADIATION INSIDE APPARENT HORIZON IN QUANTUM-GRAVITY

We study black hole radiation inside the apparent horizon in quantum g ravity. First we perform a canonical quantization for a spherically sy mmetric geometry, where one of the spatial coordinates is treated as t he time variable, since we would like to consider the interior region of a black hole. Next this rather general formalism is applied for a s pecific model, where the ingoing Vaidya metric is used as a simple mod el of an evaporating black hole. Following Tomimatsu's idea, we will a nalytically solve the Wheeler-DeWitt equation in the vicinity of the a pparent horizon and see that the mass-loss rate of a black hole due to thermal radiation is equal to the result obtained by Hawking in his s emiclassical treatment. The present formalism may have a wide applicat ion in quantum gravity inside the horizon of a black hole to problems such as mass inflation, strong cosmic censorship, etc.