Abstract
The mass of the Schwarzschild black hole, an observable quantity, is defined as a dynamical variable, while the corresponding conjugate is considered as a generalized momentum. Then a two-dimensional phase space is composed of the two variables. In the two-dimensional phase space, a harmonic oscillator model of the Schwarzschild black hole is obtained by a canonical transformation. By this model, the mass spectrum of the Schwarzschild black hole is firstly obtained. Further the horizon area operator, quantum area spectrum and entropy are obtained in the Fock representation. Lastly, the wave function of the horizon area is derived also.
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References
Bekenstein J D. Black hole and entropy. Phys Rev D, 1973, 7(8): 2333–2346
Hawking S W. Particle creation by black hole. Commun Math Phys, 1975, 43(3): 199–220
Zhu J Y, Zhang J H, Zhao Z. Hawking radiation of charged Dirac particle in Vaidya-Bonner space-time. Sci China A-Math Phys Astron, 1995, 38(2): 217–226
Li X, Zhao Z. Entropy of a Vaidya black hole. Phys Rev D, 2000, 62(10): 104001-1–4
’t Hooft G. On the quantum structure of a black hole. Nucl Phys, 1985, 256: 727–745
Liu W B, Zhao Z. Entropy of the Dirac field in a Kerr-Newman black hole. Phys Rev D, 2000, 61: 063003-1–4
Gao C J, Shen Y G. Entropy of three-dimensional BTZ black holes. Sci China Ser G-Phys Mech Astron, 2004, 47(3): 277–283
Wu Z C, Xu D H. Constrained instanton and black hole creation. Sci China Ser G-Phys Mech Astron, 2004, 47(3): 293–309
Li C A. Formula for black hole’s Planck absolute entropy. Acta Phys, 2001, 50(5): 986–989
Yang S Z, Li H L, Jiang Q Q, et al. The research on the quantum tunneling characteristics and the radiation spectrum of the stationary axisymmetric black. Sci China Ser G-Phys Mech Astron, 2007, 50(2): 249–260
Liu C Z. The information entropy of a static dilaton black hole. Sci China Ser G-Phys Mech Astron, 2008, 51(2): 113–125
Bekenstein J D, Gour G. Building blocks of a black hole. Phys Rev D, 2002, 66(2): 024005-1–7
Louko J, Mäkelä J. Area spectrum of the Schwarzschild black hole. Phys Rev D, 1996, 54(8): 4982–4996
Mäkelä J, Repo P. Quantum-mechanical model of the Rerssner-Nordström black hole. Phys Rev D, 1998, 57(8): 4889–4916
Li C A, Su J Q. The resonance model and quantum area spectrum of Kerr-Newman black hole. Acta Phys, 2006, 55(9): 4433–4436
Jiang J J, Li C A. Quantum area spectrum of Kerr black hole and the smallest mass of micro-black hole. Acta Phys, 2005, 54(8): 3958–3961
Gour G, Medved A J M. Quantum spectrum for a Kerr-Newman black hole. Class Quantum Grav, 2003, 20: 1661–1671
Li X, Shen Y G. Quantizing the de Sitter Space-time. Phys Lett B, 2004, 602: 226–230
Barvinsky A, Das A, Kunstatter G. Quantum mechanics of charged black holes. Phys Lett B, 2001, 517: 415–420
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Supported by the National Natural Science Foundation of China (Grant No. 10773002) and the Natural Research Foundation of Heze University (Grant No. XY05WL02)
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Li, C., Su, J., Jiang, J. et al. The dynamical model and quantization of the Schwarzschild black hole. Sci. China Ser. G-Phys. Mech. Astron. 51, 1861–1867 (2008). https://doi.org/10.1007/s11433-008-0170-y
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DOI: https://doi.org/10.1007/s11433-008-0170-y