Black Hole Radiation inside Apparent Horizon in Quantum Gravity

Details Black Hole Radiation inside Apparent Horizon in Quantum Gravity Black Hole Radiation inside Apparent Horizon in Quantum Gravity

1996-10-24

arxiv.org/abs/gr-qc/9610055v1

Prog.Theor.Phys. 97 (1997) 233-242

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, phyzzx

Scientific paper

10.1143/PTP.97.233

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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