黑洞熵统计起源的研究

发布时间：2018-05-24 18:06

本文选题：deSitter黑洞时空 + 统计熵　；参考：《湖南科技大学》2011年硕士论文

【摘要】：自黑洞被广义相对论预言以来,研究者们在理论及观测上都做了大量的工作,试图揭示黑洞的本质及黑洞熵的统计起源。本文主要研究利用修正到Planck长度任意阶的的态密度方程计算静态黑洞时空的统计熵。在第一章中,我们首先介绍黑洞的起源及其形成过程,接着介绍黑洞学的基本概念和基本理论,随后讨论黑洞熵的统计起源。在第二章中,我们对求解黑洞熵的两种模型(砖墙模型和薄膜模型)进行综述,并介绍两种模型的适用条件;再以Schwarzschild黑洞时空及静态deSitter黑洞时空为例运用此两种模型求解标量场的熵值,得出黑洞时空量子场的统计熵与其表面积成比例的结论;最后总结两种模型的特点并分析在研究过程中所遇到的截断因子及熵的发散问题。第三章主要介绍笔者自己的工作。首先介绍了位置与动量的广义测不准关系,并由此得到位置的最小不确定度;再根据推广的对易关系对相应的微观状态态密度方程作出修正,运用修正后的态密度方程得到的黑洞外物质场的量子态数在视界处是收敛的;最后将修正到Planck长度任意阶的态密度方程应用到Schwarzschild-deSitter黑洞时空标量场统计熵的计算及Reissner-Nordstrom黑洞时空Dirac场统计熵的计算中去。
[Abstract]:Since the black hole was predicted by general relativity, researchers have done a lot of work in theory and observation, trying to reveal the nature of black hole and the statistical origin of black hole entropy. In this paper, the statistical entropy of static black hole space-time is calculated by using the modified density of states equation with arbitrary order of Planck length. In the first chapter, we first introduce the origin and formation process of black hole, then introduce the basic concept and theory of black hole science, then discuss the statistical origin of black hole entropy. In the second chapter, we summarize the two models (brick wall model and thin film model) for solving black hole entropy, and introduce the applicable conditions of the two models. Then taking Schwarzschild black hole space-time and static deSitter black hole space-time as examples, the entropy of scalar field is solved by using these two models, and the conclusion that the statistical entropy of black hole space-time quantum field is proportional to its surface area is obtained. Finally, the characteristics of the two models are summarized and the problems of truncation factor and entropy divergence are analyzed. The third chapter mainly introduces the author's own work. Firstly, the generalized uncertainty relation between position and momentum is introduced, and the minimum uncertainty of position is obtained, and then the corresponding microcosmic state density equation is modified according to the generalized commutative relation. The number of quantum states in the field of matter outside the black hole obtained by the modified density of state equation is convergent at the horizon. Finally, the density of states equation modified to any order of Planck length is applied to calculate the statistical entropy of the scalar field of Schwarzschild-deSitter black hole and the statistical entropy of Dirac field of Reissner-Nordstrom black hole.
【学位授予单位】：湖南科技大学
【学位级别】：硕士
【学位授予年份】：2011
【分类号】：P145.8

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