Black Hole Radiation inside Apparent Horizon in Quantum Gravity

TL;DR

This paper develops a quantum gravity framework to analyze black hole radiation inside the apparent horizon, deriving a mass-loss rate consistent with Hawking radiation through analytical solutions of the Wheeler-DeWitt equation.

Contribution

It introduces a canonical quantization approach for spherically symmetric black hole interiors and analytically solves the Wheeler-DeWitt equation near the apparent horizon.

Findings

Mass-loss rate matches Hawking's semiclassical result

Analytical solutions of Wheeler-DeWitt equation near the horizon

Framework applicable to various quantum gravity phenomena inside black holes

Abstract

We study a black hole radiation inside the apparent horizon in quantum gravity. First we perform a canonical quantization for spherically symmetric geometry where one of the spatial coordinates is dealt 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 solve analytically the Wheeler-DeWitt equation in the vicinity of the apparent horizon and see that mass-loss rate of a black hole by 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 such as mass inflation and strong cosmic censorship etc.