Abstract:
The physical idea of thin film model improved from brick-wall model is more direct and clearer than brick-wall model and gives prominence to the significance of the event horizon serving as the characteristic surface of a static or stationary black hole. To remove the divergence of the density of states, an ultraviolet cutoff factor is also introduced into the thin film model. The cutoff is introduced artificially and it has not been understood clearly up to now. There is an indication in a reference that the divergence can be removed without any cutoff when the generalized uncertainty relation is used to calculate black hole entropy. In this paper, thin film model without cutoff and the essential difference between the thin film model without cutoff and the thin film model with cutoff are expounded by the example of calculating the entropy of spherically symmetric static black hole Dirac field.

Abstract:
By using of the brick-wall method,we calculate the free energy and the entropy of Dirac spinor field in Schwarzschild black hole-It shows that the entropy of Dirac field is proportional to the area of black hole horizon and the entropy of Dirac field is 7/2 times that of Klein-Gordon field-

Abstract:
Black hole entropy has been shown by 't Hooft to diverge at the horizon. The region near the horizon is in a thermal state, so entropy is linear to energy which consequently also diverges. We find a similar divergence for the energy of the reduced density matrix of relativistic and non-relativistic field theories, extending previous results in quantum mechanics. This divergence is due to an infinitely sharp division between the observable and unobservable regions of space, and it stems from the position/momentum uncertainty relation in the same way that the momentum fluctuations of a precisely localized quantum particle diverge. We show that when the boundary between the observable and unobservable regions is smoothed the divergence is tamed. We argue that the divergence of black hole entropy can also be interpreted as a consequence of position/momentum uncertainty, and that 't Hooft's brick wall tames the divergence in the same way, by smoothing the boundary.

Abstract:
In this article we study relationship between three measures of distinguishability of quantum states called as divergence, relative entropy and the substate property.

Abstract:
We investigate the cause of the divergence of the entanglement entropy for the free scalar fields in $(1+1)$ and $(D + 1)$ dimensional space-times. In a canonically equivalent set of variables, we show explicitly that the divergence in the entanglement entropy of the continuum field in $(1 + 1)-$ dimensions is due to the accumulation of large number of near-zero frequency modes as opposed to the commonly held view of divergence having UV origin. The feature revealing the divergence in zero modes is related to the observation that the entropy is invariant under a hidden scaling transformation even when the Hamiltonian is not. We discuss the role of dispersion relations and the dimensionality of the space-time on the behavior of entanglement entropy.

Abstract:
Using the improved brick-wall film model, we calculated the entropy of Dirac field in a generalized non-stationary spherically symmetric black hole with charge. From the point of view of the model, these entropies are nothing but the entropy of the black hole. The result showed that this entropy is proportion to the area of event horizon.

Abstract:
The generalized uncertainty relation is considered in the new equation of state density. Using the WKB approximation, Dirac field entropy of the horizon of the black hole with an internal global monopole is calculated directly. The result shows that the black hole entropy is proportional to the horizon area, which brings to light the relationship between the black hole entropy and the entropy of quantum state near the event horizon. The difference from the brick-wall model is that the present result is convergent without any cutoff. It is indicated that this method can be used to calculate the entropy of the scale field of black hole, and it can be extended to calculate the entropy of Dirac field.

Abstract:
We are familiar with Dirac equation in flat space by which we can investigate the behaviour of half-integral spin particle. With the introduction of general relativistic effects the form of the Dirac equation will be modified. For the cases of different background geometry like Kerr, Schwarzschild etc. the corresponding form of the Dirac equation as well as the solution will be different. In 1972, Teukolsky wrote the Dirac equation in Kerr geometry. Chandrasekhar separated it into radial and angular parts in 1976. Later Chakrabarti solved the angular equation in 1984. In 1999 Mukhopadhyay and Chakrabarti have solved the radial Dirac equation in Kerr geometry in a spatially complete manner. In this review we will discuss these developments systematically and present some solutions.

Abstract:
Using the Tortoise coordinate transformation and the Dirac field equation near the event horizon, the Hawking temperature of Kinnersley black hole is obtained. Meanwhile, adopting thin film brick-wall model, the entropy of Kinnersley black hole is calculated. The entropy near the event horizon is shown to be the entropy of black hole by regulating the cut-off parameter and the thin film's thickness properly. The results show that the entropy of the black hole is proportional to the area of the event horizon.

Abstract:
By using the thin film model,which is based on the brick-wall method,the entropy of the Dirac field in a general spherically symmetric and charged evaporating black hole is calculated.The conclusion that black hole entropy is proportional to its horizon area can still be applied by regulating the cutoff,which is time dependent.