真空无奇点黑洞的拟正则模
发布时间：2018-12-17 15:40
【摘要】：黑洞是广义相对论最伟大的预言之一。然而,黑洞存在许多不可思议的物理现象,其中最为人所知的是黑洞的中央奇点的存在。当奇点存在时物理定律在这里失效,但是根据现有的广义相对论理论,存在奇点的黑洞解又是不可避免的,例如史瓦西黑洞,R-N黑洞和Kerr黑洞等。在广义相对论中,寻找中心不存在奇点的黑洞的问题是非常重要的。因此,一些量子模型和几何的模型来克服奇点的问题。其中后一种将是我们这里要讨论的理论模型,它以Bardeen黑洞为代表。为了研究隐藏在视界后面的黑洞的性质,对黑洞时空作扰动是不错的了解视角。通过视界的扰动会产生一些物理现象,其中包括了我们这里要研究的拟正则模,从而我们能分析黑洞在扰动下的稳定性。黑洞的拟正则模是复数,它携带了黑洞在扰动后如何恢复稳定的信息,它的数值与黑洞时空的性质和扰动的类型有关。本文研究带有de Sitter中心的球对称黑洞在标量场扰动下的拟正则模。几何上来讲,这种黑洞在半径很大的时候趋近与史瓦西解形式,在趋于0的时候是de Sitter解形式的。在这里我们通过变化参数(它与宇宙学常数有关),角量子数,泛音数和黑洞质量来研究这个黑洞的拟正则模。根据6阶WKB近似的计算结果,我们发现拟正则模在随的变化出现极大值和极小值,同时对于一定范围的,当拟正则模随泛音数n变化时也会出现极值现象,这是值得关注的。这个爱因斯坦方程的精确解析解不带电,没有用到电动力学或其他的理论,所以通过对真空无奇点黑洞的拟正则模的研究,将有助于我们对不带电的无奇点黑洞的性质的了解。
[Abstract]:Black holes are one of the greatest prophecies of general relativity. However, black holes have many incredible physical phenomena, among which the existence of central singularities of black holes is best known. When the singularity exists, the laws of physics fail here, but according to the existing theory of general relativity, the solution of the black hole with singularity is inevitable, such as the Schwarzie black hole, R-N black hole and Kerr black hole, etc. In general relativity, the problem of finding black holes with no singularities in the center is very important. Therefore, some quantum models and geometric models to overcome the singularity problem. The latter will be the theoretical model we will discuss here, as represented by the Bardeen black hole. In order to study the properties of black holes hidden behind the event horizon, it is a good way to understand the space-time perturbation of black holes. Some physical phenomena can be generated by the perturbation of the event horizon, including the quasi-regular modes that we are going to study here, so that we can analyze the stability of black holes under perturbation. The quasi-regular mode of a black hole is a complex number, which carries information on how the black hole recovers stability after disturbance. Its numerical value is related to the properties of the space-time and the type of perturbation of the black hole. In this paper, the quasi-regular modes of a spherically symmetric black hole with de Sitter center under scalar field perturbation are studied. Geometrically, the black hole approaches to the Schwarzie solution form when its radius is very large, and is de Sitter solution form when it tends to 0. Here we study the quasi-regular modes of the black hole by varying the parameters (which are related to cosmological constants), angular quantum numbers, generalized sound numbers, and the mass of the black hole. According to the results of the WKB approximation of order 6, we find that the maximum and minimum value of quasi-regular modules appear with the change of the number of overtones n, and for a certain range, the phenomenon of extreme values will also appear when the quasi-regular modules change with the number of overtones n, which is worthy of attention. The exact analytical solution of this Einstein equation is not charged and does not use electrodynamics or other theories. Therefore, the study of quasi-regular modes of a vacuum black hole without singularities will help us to understand the properties of an uncharged black hole without singularities.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P145.8
本文编号：2384401
[Abstract]:Black holes are one of the greatest prophecies of general relativity. However, black holes have many incredible physical phenomena, among which the existence of central singularities of black holes is best known. When the singularity exists, the laws of physics fail here, but according to the existing theory of general relativity, the solution of the black hole with singularity is inevitable, such as the Schwarzie black hole, R-N black hole and Kerr black hole, etc. In general relativity, the problem of finding black holes with no singularities in the center is very important. Therefore, some quantum models and geometric models to overcome the singularity problem. The latter will be the theoretical model we will discuss here, as represented by the Bardeen black hole. In order to study the properties of black holes hidden behind the event horizon, it is a good way to understand the space-time perturbation of black holes. Some physical phenomena can be generated by the perturbation of the event horizon, including the quasi-regular modes that we are going to study here, so that we can analyze the stability of black holes under perturbation. The quasi-regular mode of a black hole is a complex number, which carries information on how the black hole recovers stability after disturbance. Its numerical value is related to the properties of the space-time and the type of perturbation of the black hole. In this paper, the quasi-regular modes of a spherically symmetric black hole with de Sitter center under scalar field perturbation are studied. Geometrically, the black hole approaches to the Schwarzie solution form when its radius is very large, and is de Sitter solution form when it tends to 0. Here we study the quasi-regular modes of the black hole by varying the parameters (which are related to cosmological constants), angular quantum numbers, generalized sound numbers, and the mass of the black hole. According to the results of the WKB approximation of order 6, we find that the maximum and minimum value of quasi-regular modules appear with the change of the number of overtones n, and for a certain range, the phenomenon of extreme values will also appear when the quasi-regular modules change with the number of overtones n, which is worthy of attention. The exact analytical solution of this Einstein equation is not charged and does not use electrodynamics or other theories. Therefore, the study of quasi-regular modes of a vacuum black hole without singularities will help us to understand the properties of an uncharged black hole without singularities.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：P145.8
【参考文献】
相关硕士学位论文 前1条
1 杨彬;渐近安全引力中黑洞的拟正则模[D];上海师范大学;2012年
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