Hawking Radiation of a Charged Black Hole in Quantum Gravity

Abstract

We study black hole radiation of a Reissner-Nordstrom black hole with an electric charge in the framework of quantum gravity. Based on a canonical quantization for a spherically symmetric geometry, under physically plausible assumptions, we solve the Wheeler-De Witt equation in the regions not only between the outer apparent horizon and the spatial infinity but also between the spacetime singularity and the inner apparent horizon, and then show that the mass loss rate of an evaporating black hole due to thermal radiation agrees with the semiclassical result when we choose an integration constant properly by physical reasoning. Furthermore, we also solve the Wheeler-De Witt equation in the region between the inner Cauchy horizon and the outer apparent horizon, and show that the mass loss rate of an evaporating black hole has the same expression. The present study is the natural generalization of the case of a Schwarzschild black hole to that of a charged Reissner-Nordstrom black hole.