High Dimensional And Low-dimensional Dynamics Of Black Hole Entropy And The Generalized Uncertainty Relation On The Amendments To The Black Hole Entropy

This article includes two parts. The first one presents the characters of black hole and the origin of black hole entropy coupled with several kinds of methods calculating the black hole entropy. The second part is some work about entropy of black hole guided by my tutor .Five chapters are in this article: the chapter one provides the whole introduction focusing on the occurrence of black hole concept and characters of black hole entropy. The meaning of studying black hole entropy and the achievement it have had were also displayed. It shows in details the methods of calculating the black hole entropy and the problem produced during the study. The chapter two presents the calculation of high dimensions non-stationary black hole entropy. In the recent study of space-time, high dimensions is a unavoidable problem. We overcome some difficulty in mathematics and calculate the free energy and the entropy of black hole in high dimensions space-time. The result shows that the relation between the entropy and horizon area of black hole is still as same as in four dimensions space-time which the former is direct proportion to the later while the coefficient is different due to different dimensions. In the chapter three a low dimensions non-stationary black hole entropy is calculates. There are many too difficult problems to result in studying for four and high dimensions non-stationary black hole, therefore in order to get further information about black hole we choose low dimensions non-stationary black hole as our research item. When we deal it in low dimensions space-time some questions are simplified. The result shows that the entropy of black hole must exist only if the horizon of black hole exists and the entropy of black hole in low space-time is still proportional to the horizon area of the black hole. The chapter four is to modify the entropy using the generalized uncertainty relation. In the previous works one must adopt some cutoffs in brick wall mode to avoid the divergent entropy. It needs a radial cutoff in static and spherical black hole ,But for a rotational black hole because of the existence of the angular velocity, it need not only a radial cutoff but also an angular cutoff to avoid the divergence.However it is rather unnatural. In this chapter we take account the influence of quantum gravity and calculate the entropy of a rotational black hole again. When the generalized uncertainty relation is considered the new equation of quantum state density is obtained based on Liouville's theorem. Therefore, we find the quantum states density becomes finite near the horizon of black hole and the divergence of entropy in the brick wall model is removed without any unnatural cutoff.