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Black Hole Radiation inside Apparent Horizon in Quantum Gravity

Akio Hosoya·Ichiro Oda
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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.

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Akio Hosoya, Ichiro Oda. 1996-10-24. Black Hole Radiation inside Apparent Horizon in Quantum Gravity. https://doi.org/10.1143/ptp.97.233

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