Search

Quantum mechanics model of Schwarzschild black hole is obtained by putting the classical Hamilton into Schrodinger equation. The results show that quantum mechanics model of Schwarzschild black hole is a harmonic oscillator containing perturbation in the general case. It is related to the microscopic quantum potential. Under special cases, it can be simplified into a standard model of the harmonic oscillator. The energy spectrum, event horizon area and wave function of Schwarzschild black hole are strictly obtained by the second quantization. The quantization of black hole is also proved.

Based on the theory of loop quantum gravitation and the first law of black hole thermodynamics, the real part of the quasi-regular mode frequency of Kerr black hole is derived strictly, and the quasi-regular mode frequency spectrum of Kerr black hole is obtained. The results show that there are two families of quasi-rnormal mode frequencies of Kerr black holes, one of which is related to the parameters of the event horizon outside the black hole, while the other is only dependent on the parameters of the event horizon of Schwarzschild black holes. Our results are in good agreement with Hod’s analytical results. By choosing the minimum spin, we confirmed the present results of quasi-normal mode frequencies in Kerr black holes.

The scatting probability of scalar particles near the event horizon is obtained by solving Klein-Gordon equation in curved space-time. By considering the reaction of a black hole radiation in space-time background, we find that Hawking radiation is not a strictly pure thermal-spectrum and scatting probability is related to the B-H entropy change of black hole. The statistical entropy of black hole is calculated based on the relations between entropy and thermodynamic probability of a macroscopic state in statistical equilibrium. The results show that the statistical entropy of black hole without using any truncation factor is proportional to the area of event horizon.

The minimum interval of event horizon area of Rerssner-Nordstrom black hole was calculated via using the loop quantum gravity theory. Based on the first law of black hole thermodynamics, the real part of quasi-normal modes frequency of the black hole was calculated. The expression of asymptotically quasi-normal mode frequency of Rerssner-Nordstrom black hole was deduced strictly. By analyzing the value of the minimum spin j m i n , the two families of quasi-normal mode spectra of the charged black hole were obtained for j m i n = 1/2 and j m i n = 1 respectively. Our conclusion is in complete agreement with the analytical results of Hod. Our results provide the theoretical basis for the source of the real part of the quasi-normal mode frequency of the black hole.

By constructing the four-dimensional phase space based on the observable physical quantity of Kerr black hole and gauge transformation, the Kerr black hole entropy in the phase space was obtained. Then considering the corresponding mechanical quantities as operators and making the operators quantized, entropy spectrum of Kerr black hole was obtained. Our results show that the Kerr black hole has the entropy spectrum with equal intervals, which is in agreement with the idea of Bekenstein. In the limit of large event horizon, the area of the adjacent event horizon of the black hole have equal intervals. The results are in consistent with the results based on the loop quantum gravity theory by Dreyer et al.

In this paper, we builded the thermodynamics model of black hole based on the method of York. We obtained the reduced temperature reciprocal function using the action of the system. We studied the phase structure of black holes and Hawking-Page phase transition. We obtained the first order phase transition and critical values of black hole in Rerssner-NordstrOm space time. The results showed that only when two-phase coexistence appeared only when |q| < |qc|.

By use of the radiant emittance near the event horizon of static spherically symmetric black hole, the radiation field around the black hole was studied and found the generalized Stefan Boltzmann coefficient σ of thermal radiation near the event horizon is much greater than the flat space-time blackbody radiation. For Schwarzschild black hole, σ will increased as the black hole mass increases. For Reissner-Nordstrom black hole, σ has some relation with the quality and the charges of the black hole. Thermal particle model was proposed creatively to study the radiation power and radiant energy flux of static spherically symmetric black hole, found when η take the inherent thickness, for all Schwarzschild black hole the radiation power are the same and the radiant energy flux is inversely proportional to the square of the distance from observer to the black hole, for Reissner-Nordstrom black hole the radiation power is associated with the quality and the charge of the black hole. When given the mass and charges of the black hole, the radiant energy flux is inversely proportional to the square of the distance from observer to the black hole.

By the thin film model of the black hole and the assumption of the local thermal equilibrium, the instantaneous radiation energy flux and radiation power of the slowly changing Vaidya black hole have been studied. The result has been obtained that the thermal radiation of the Vaidya black hole satisfies the generalized Stefan-Boltzmann law. When the cut-off distance and the thin film thickness are both fixed, the instantaneous radiation energy flux of the scalar field near the event horizon of the Vaidya black hole is not only related to the black hole mass, but also to the rate of the change of its event horizon and the average effusion velocity of the radiation particles in the thin film. While its instantaneous radiation power is related to the rate of the change of the event horizon and the average radial effusion velocity of the radiation particles in the thin film. These results indicate that the gravitational field around the black hole and the change of its event horizon will both affect the thermal radiation of the black hole.

Applying the entropy density near the event horizon, we obtained the result that the radiation energy flux of the black hole is always proportional to the quartic of the temperature of its event horizon. That is to say, the thermal radiation of the black hole always satisfies the generalized Stefan–Boltzmann law. The derived generalized Stefan–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 which is related to the black hole mass, the kinds of radiation particles and space–time metric near the event horizon. In this paper, we have put forward a thermal particle model in curved space–time. By this model, the result has been obtained that when the thin film thickness and the cut-off distance are both fixed, the radiation energy flux received by observer far away from the Schwarzschild black hole is proportional to the average radial effusion velocity of the radiation particles in the thin film, and inversely proportional to the square of the distance between the observer and the black hole.

Applying quantum tunneling method, this paper has studied the Hawking radiation of Garfinkle-Horowitz-Stromingen dilaton black hole. In this way, the emission rates of massless particles and massive particles tunneling across the event horizon of black holes is obtained. The result shows that the radiation spectrum of these two different kinds of outgoing particles is related to the change of Bekenstein-Hawking entropy, which is no longer precisely thermal.