Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1993-08-26
Prog.Theor.Phys. 90 (1993) 861-870
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
18 pages, DPNU-93-31
Scientific paper
10.1143/PTP.90.861
By using the minisuperspace model for the interior metric ofstatic black holes, we solve the Wheeler-DeWitt equation to study quantum mechanics of the horizon geometry. Our basic idea is to introduce the gravitational mass and the expansions of null rays as quantum operators. Then, the exact wave function is found as a mass eigenstate, and the radius of the apparent horizon is quantum-mechanically defined. In the evolution of the metric variables, the wave function changes from a WKB solution giving the classical trajectories to a tunneling solution. By virtue of the quantum fluctuations of the metric evolution beyond the WKB approximation, we can observe a static black hole state with the apparent horizon separating from the event horizon.
Konno S.
Nakamura Kazuo
Shiro Y.
Tomimatsu Akira
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