黑洞温度修正与黑洞寿命的研究

发布时间：2018-01-18 10:28

本文关键词：黑洞温度修正与黑洞寿命的研究　出处：《广州大学》2013年硕士论文　论文类型：学位论文

【摘要】：黑洞的霍金辐射是理论物理学科的一个重要发现，它是广义相对论、量子力学以及热力学的结合产物。1970年霍金突破性的提出面积定理，指出黑洞的表面积随着时间的推移只会增大而不会减小。1972年贝肯斯坦提出，黑洞是一个热力学系统，黑洞的表面积就是黑洞的熵，因此黑洞的视界表面积与黑洞的熵成正比[1]。1974年霍金利用弯曲时空的量子场论，从理论上证明黑洞具有热辐射，即著名的霍金辐射，并给出了黑洞的温度。霍金的发现进一步证实了黑洞并不是一个死了的恒星，它正在演化，是一个热力学系统[2]。对黑洞熵的研究是理论物理学界感兴趣的课题之一。为了讨论其统计起源，1985年，t‘Hooft提出了计算黑洞熵的砖墙模型[3-8]，2000年，北京师范大学引力组提出了改进的砖墙模型[9,10]---薄层模型[11,14]。这种模型推断黑洞熵来自视界面附近一个薄层的量子场的贡献。无论是砖墙模型还是改进的薄层模型，都认为黑洞熵正比于黑洞视界面积。最近的研究表明，考虑到视界附近的量子效应，黑洞熵应增加两个高阶修正项[15,17]，利用修正之后的黑洞熵公式就可以对黑洞的温度进行修正，并且在修正黑洞温度的情况下可以利用斯特藩-玻尔兹曼定律重新计算黑洞寿命。利用黑洞熵的高阶修正还可以讨论由此而产生的一系列相关问题。本文在总结了硕士研究生阶段的研究工作，即在利用黑洞熵量子修正的前提条件下，对黑洞温度以及黑洞寿命变化进行了修正性的推导计算。研究发现，黑洞蒸发到普朗克质量时，温度将出现无限大，再减小质量时将出现负温，此时黑洞熵也将出现极小值。本文共分三章，，其具体内容包括：第一章简要介绍了黑洞研究的历史以及霍金辐射机制的由来以及研究背景，并介绍了量子隧穿的几种模型的理论基础以及其发展历史。第二章在黑洞熵具有量子修正的情况下，对黑洞温度进行更加精确的修正，并对由此引起的黑洞寿命变化做了重新计算。另外还讨论了在黑洞质量变化时，相对应的黑洞温度以及黑洞热容的变化趋势。第三章对本文的工作进行总结和展望，并提出了今后工作的相关设想。
[Abstract]:Hawking radiation from black holes is an important discovery in theoretical physics. It is a combination of general relativity quantum mechanics and thermodynamics. In 1970 Hawking put forward a breakthrough area theorem. It is pointed out that the surface area of black hole will only increase but not decrease with time. In 1972, Beckenstein proposed that black hole is a thermodynamic system, and the surface area of black hole is the entropy of black hole. Therefore, the surface area of the event horizon of the black hole is proportional to the entropy of the black hole. [In 1974 Hawking made use of the quantum field theory of curved spacetime to prove theoretically that a black hole has heat radiation known as Hawking radiation. And the temperature of the black hole is given. Hawking's discovery further proves that the black hole is not a dead star, it is evolving, it is a thermodynamic system. [2]. The study of black hole entropy is one of the topics of interest to theoretical physics. In 1985, in order to discuss its statistical origin, Hooft proposed a brick wall model for calculating black hole entropy. [In 2000, the Gravity Group of Beijing normal University proposed an improved brick wall model. [9 ~ 10] -Thin-layer model. [The model inferred that the black hole entropy was contributed by a quantum field of a thin layer near the visual interface, whether it was a brick wall model or an improved thin layer model. It is believed that the entropy of black hole is proportional to the area of event horizon. Recent studies have shown that considering the quantum effect near the event horizon, the entropy of black hole should be increased by two higher-order correction terms. [By using the modified black hole entropy formula, the temperature of the black hole can be corrected. Furthermore, the black hole lifetime can be recalculated by using Staffan-Boltzmann 's law when the temperature of the black hole is corrected, and a series of related problems can be discussed by using the higher-order correction of the black hole entropy. In this paper, we summarize the research work of the master's degree, that is, under the precondition of using the black hole entropy quantum correction, we calculate the black hole temperature and the black hole lifetime change. When the black hole evaporates to Planck mass, the temperature will be infinite, and then the mass will be negative, and the black hole entropy will be minimized. This paper is divided into three chapters, the specific contents of which are as follows: The first chapter briefly introduces the history of black hole research, the origin and background of Hawking radiation mechanism, and introduces the theoretical basis and development history of several models of quantum tunneling. In the second chapter, when the entropy of black hole has quantum correction, the temperature of black hole is corrected more accurately, and the black hole lifetime change caused by it is recalculated. In addition, when the mass of black hole changes, we also discuss the change of black hole mass. The corresponding change trend of black hole temperature and black hole heat capacity. The third chapter summarizes and prospects the work of this paper, and puts forward some related ideas for future work.
【学位授予单位】：广州大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：P145.8

【参考文献】