Black hole radiation inside apparent horizon in quantum gravity

We study black hole radiation inside the apparent horizon in quantum gravity. First we perform a canonical quantization for a spherically symmetric geometry, where one of the spatial coordinates is treated as the time variable, since we would like to consider the interior region of a black hole. Next this rather general formalism is applied for a specific model, where the ingoing Vaidya metric is used as a simple model of an evaporating black hole. Following Tomimatsu's idea, we will analytically solve the Wheeler-DeWitt equation in the vicinity of the apparent 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 semiclassical treatment. The present formalism may have a wide application in quantum gravity inside the horizon of a black hole to problems such as mass inflation, strong cosmic censorship, etc.