Using the related formula of dynamic black holes, the instantaneous radiation energy density of the general spherically symmetric charged dynamic black hole and the arbitrarily accelerating charged dynamic black hole is calculated. It is found that the instantaneous radiation energy density of black hole is always proportional to the quartic of the temperature of event horizon in the same direction. The proportional coefficient of generalized Stefan-Boltzmann is no longer a constant, and it becomes a dynamic coefficient that is related to the event horizon changing rate, space-time structure near event horizon and the radiation absorption coefficient of the black hole. It is shown that there should be an internal relation between the gravitational field around black hole and its thermal radiation. entropy density, thin film model, instantaneous radiation energy density, generalized Stenfan-Boltzmann coefficient, event horizonSince Bekenstein and Hawking suggested that the entropy of black holes is proportional to its area of event horizon [1,2] , there have been many methods which were used to calculate the entropy of black holes [3][4][5][6] . One of them is the brick-wall model proposed by 't Hooft [3] . Several years ago, the brick-wall was improved to the thin film model [7][8][9] . Based on this thin film model, the entropy of black holes comes from the quantum field in the infinitesimal layer around event horizon. So the thin film model can be used to study dynamic black hole by using local thermal equilibrium near event horizon. The entropy of many dynamic black holes has been calculated by the thin film model [10][11][12][13][14][15] . Where there is event horizon, there should be entropy of black holes and Hawing radiation [16] . Recently, the research on the quantum tunneling of black holes shows that the quantum tunneling rate is related to the change of entropy of black holes [17,18] . It shows that there must be an internal relation between the entropy and the thermal radiation of black holes. In ref.[19], the radiation energy density of black holes was studied by using the statistic entropy of Dirac field in the static spherically symmetric black holes. It is drawn that the radiation energy density is always proportional to quartic of the temperature of event horizon. In ref.[20], the dynamic black hole is
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.loop quantum gravity, quasinormal mode, quantum area spectrum, black hole entropy, quantization Ever since Hawking proved that the black hole has thermal radiation, much pioneer work has been done on the black hole physics, especially on the black hole entropy. Furthermore, it has long been argued by Bekenstein that the proportionality between entropy and area [1] , for large classical black holes, can be justified from the adiabatic invariance properties of horizon area. In 1974, Bekenstein further suggested that the horizon area, when quantized, should have a discrete, equidistant spectrum in the large horizon limit [2] :where l pl is the Planck length, N integer and k a pure number of order one. Because of the proportional relation between entropy and area, it is also important to study the black hole entropy, besides the quantum area spectrums, which has important practical significance to understand the intrinsic essence and structure of the black hole entropy [3] . Furthermore the black hole entropy would have a discrete spectrum, a property that might also be expected if the black hole entropy is associated with the number of microstates compatible with a given macrostate. So the quantization of horizon area must lead to the quantization of the black hole entropy [4] . Loop quantum gravity is a non-perturbative canonical quantum gravity [5] , which can offer a quantum canonical description to quantum horizon degrees of freedom [6] .
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. black hole, Fock representation, mass spectrum, quantum area spectrum, wave function of horizon area After Bekenstein's [1] and Hawking's [2] initial work, the thermodynamics and the statistic mechanics of black holes have been one of the important research areas. Especially in recent years, many authors have already obtained some interesting results on the thermal radiation and the entropy of black holes [3][4][5][6][7][8][9][10][11] . Many conclusions with various different methods revealed that the black hole's entropy is proportional to the horizon area. According to this idea, it is significant to establish an accurate quantum model of black holes, realize space-time quantization, and study quantum spectrums of the black hole horizon area. These topics are active research fields at present. Bekenstein (1974) firstly argued that the possible eigen values of the black hole's horizon area were [9] 2 pl ,where n is an integer, γ is a pure number of one order and 3 pl l Gc − = is the Planck's length.In order to approve the Bekenstein's hypothesis, many authors established different quantum models of black holes [12][13][14] , and the quantum area spectrums were obtained. Louko and Mäkelä [13] derived the quantum area spectrum of the Schwarzschild black hole's horizon:
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.
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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.