The mass of the Schwarzschild black hole, an observable quantity, is defined as a dynamical variable, while the corresponding conjugate is considered as a general- ized momentum. Then a two-dimensional phase space is ...The mass of the Schwarzschild black hole, an observable quantity, is defined as a dynamical variable, while the corresponding conjugate is considered as a general- ized 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.展开更多
Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity,the minimum horizon area gap is obtained.Then the quantum area spectrum of black holes is derived an...Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity,the minimum horizon area gap is obtained.Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization.The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi.展开更多
基金the National Natural Science Foundation of China (Grant No. 10773002)the Natural Research Foundation of Heze University (Grant No. XY05WL02)
文摘The mass of the Schwarzschild black hole, an observable quantity, is defined as a dynamical variable, while the corresponding conjugate is considered as a general- ized 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.
基金Supported by the National Natural Science Foundation of China (Grant No. 10773002)
文摘Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity,the minimum horizon area gap is obtained.Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization.The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi.
