Abstract:
By using the new equation of state density derived from the generalized uncertainty relation, the number of the quantum states near event horizon is obtained, with which then the information entropy of static spherically symmetric black holes has been discussed. It is found that the divergent integral of quantum states near the event horizon can be naturally avoided if using the new equation of state density without introducing the ultraviolet cut-off. The information entropy of black holes can be obtained precisely by the residue theorem, which is shown to be proportional to the horizon area. The information entropy of black holes obtained agrees with the Bechenstein--Hawking entropy when the suitable cutoff factor is adopted.

Abstract:
Kerr black hole has only two parameters of M and J. M and J, as the general coordinates, together with their conjugate variables form a four-di mensional phase space. The quantum area spectrum of Kerr black hole is obtained by performing gauge transformations, from which we can obtain the smallest mas s of Schwarzchild black hole.

Abstract:
By employing the technique of integration within an ordered product of operators, we derive natural representations of the rotation operator, the two-mode Fourier transform operator and the two-mode parity operator in entangled state representations. As an application, it is proved that the rotation operator constructed by the entangled state representation is a useful tool to solve the exact energy spectra of the two-mode harmonic oscillators with coordinate-momentum interaction.

Abstract:
Using the related formula of dynamic black hole, we have calculated the instantaneous radiation energy density of the slowly changing dynamic Kerr--Newman black hole. It is found that the instantaneous radiation energy density of a black hole is always proportional to the quartic of the temperature of the event horizon in the same direction. By using the Hamilton--Jacobin equation of scalar particles in the curved spacetime, the spontaneous radiation of the slowly changing dynamic Kerr--Newman black hole is studied. The energy condition for the occurrence of the spontaneous radiation is obtained.

Abstract:
Using entropy density of Dirac field near the event horizon of a rectilinear non-uniformly accelerating Kinnersley black hole, the law for the thermal radiation of black hole is studied and the instantaneous radiation energy density is obtained. It is found that the instantaneous radiation energy density of a black hole is always proportional to the quartic of the temperature on event horizon in the same direction. That is to say, the thermal radiation of a black hole always satisfies the generalized Stefan--Boltzmann law. In addition, the derived generalized Stefan--Boltzmann coefficient is no longer a constant, but a dynamic coefficient related to the space--time metric near the event horizon and the changing rate of the event horizon in black holes.

Abstract:
Based on the rotation transformation in phase space and the technique of integration within an ordered product of operators, the coherent state representation of the multimode phase shifting operator and one of its new applications in quantum mechanics are given. It is proved that the coherent state is a natural language for describing the phase shifting operator or multimode phase shifting operator. The multimode phase shifting operator is also a useful tool to solve the dynamic problems of the multimode coordinate--momentum coupled harmonic oscillators. The exact energy spectra and eigenstates of such multimode coupled harmonic oscillators can be easily obtained by using the multimode phase shifting operator.

Abstract:
By the statistical entropy of the Dirac field of the static spherically symmetric black hole, the result is obtained that the radiation energy flux of the black hole is proportional to the quartic of the temperature of its event horizon. That is, the thermal radiation of the black hole always satisfies the generalised Stenfan--Boltzmann law. The derived generalised Stenfan--Boltzmann coefficient is no longer a constant. When the cut-off distance and the thin film thickness are both fixed, it is a proportional coefficient related to the space--time metric near the event horizon and the average radial effusion velocity of the radiation particles from the thin film. Finally, the radiation energy fluxes and the radiation powers of the Schwarzschild black hole and the Reissner--Nordstr m black hole are derived, separately.

Abstract:
This paper constructs the new common eigenvectors of n intermediate coordinate-momentum operators which are complete and orthonormal. The intermediate coordinate-momentum representation of a multi-particles system is proposed and applied to a general n-mode quantum harmonic oscillators system with coordinate-momentum coupling.

Abstract:
Using entropy density of scalar field near event horizon in an arbitrarily accelerating black hole with electric charge and magnetic charge,we study the law for the thermal radiation of black hole and the instantaneous radiation energy flux is obtained. It is found that the thermal radiation of a black hole always satisfies the generalized Stefan-Boltzmann's law. The proportional coefficient of generalized Stefan-Boltzmann is no longer a constant,and it becomes a dynamic coefficient that is related to the p...