Schrodinger formalism, black hole horizons, and singularity behavior
Journal Article
·
· Physical Review. D, Particles Fields
- Department of Physics, Niagara University, Niagara, New York 14109-2044 (United States) and HEPCOS, Department of Physics, SUNY at Buffalo, Buffalo, New York 14260-1500 (United States)
The Gauss-Codazzi method is used to discuss the gravitational collapse of a charged Reisner-Nordstroem domain wall. We solve the classical equations of motion of a thin charged shell moving under the influence of its own gravitational field and show that a form of cosmic censorship applies. If the charge of the collapsing shell is greater than its mass, then the collapse does not form a black hole. Instead, after reaching some minimal radius, the shell bounces back. The Schroedinger canonical formalism is used to quantize the motion of the charged shell. The limits near the horizon and near the singularity are explored. Near the horizon, the Schroedinger equation describing evolution of the collapsing shell takes the form of the massive wave equation with a position dependent mass. The outgoing and incoming modes of the solution are related by the Bogolubov transformation which precisely gives the Hawking temperature. Near the classical singularity, the Schroedinger equation becomes nonlocal, but the wave function describing the system is nonsingular. This indicates that while quantum effects may be able to remove the classical singularity, it may also introduce some new effects.
- OSTI ID:
- 21313619
- Journal Information:
- Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 12 Vol. 80; ISSN PRVDAQ; ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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