Hawking Radiation inside Black Holes in Quantum Gravity

Abstract: We study black hole radiation inside black holes within the framework of quantum gravity. First, we review on our previous work of a canonical quantization for a spherically symmetric geometry where one of the spatial coordinates is treated as the time variable, since we think of the interior region of a black hole. Based on this formalism, under physically plausible assumptions, we solve the Wheeler-De Witt equation inside the black hole, and show that the mass-loss rate of an evaporating black hole due to thermal radiation is equivalent to the result obtained by Hawking in his semi-classical approach. A remarkable point is that our assumptions make the momentum constraint coincide with the Hamiltonian constraint up to an irrelevant overall factor. Furthermore, for comparison, we solve the Wheeler-De Witt equation outside the black hole as well, and see that the mass-loss rate of an evaporating black hole has the same expression. The present analysis suggests that the black hole radiation comes from the black hole singularity. We also comment on the Birkhoff theorem in quantum gravity.