黑洞背景的粒子动力学方程及其相关问题的研究

发布时间：2018-06-17 02:59

本文选题：黑洞 + 微扰　；参考：《浙江工业大学》2017年硕士论文

【摘要】：本论文分为五章:第一章,我们介绍了黑洞微扰的概念及其发展现状。第二章,首先,我们介绍了所有奇点都是正则奇点的Fuchs型方程的奇点与解。奇点可以分为可去奇点,极点和本性奇点,正则奇点只是极点的一种特殊情形。其次,我们讨论了Heun方程,合流Heun方程等特殊微分方程的解。在给出初始条件时,级数解的系数之间满足一个三项之间的递推关系式,此递推关系式总可以看作一个三对角行列式的展开式。因此,我们讨论了三对角行列式的特点以及三对角行列式为零的方程的解。第三章,我们讨论了自旋场的动力学方程的Newman-Penrose形式,给出了类光标架的定义,得到了旋系数方程以及场方程。利用Newman-Penrose形式,研究了一般球对称时空的场方程,将该场方程分离为径向部分与角向部分,角向部分的解是自旋加权球谐函数。根据奇点的不同,径向方程可以分为不同的情形,我们将所得的径向方程进行自变量变换与函数变换,转换为超几何方程,Heun方程,合流Heun方程等特殊微分方程,并讨论了其解。第四章,我们研究了三种特殊时空背景中的场方程。由于共形引力场对重整化,暗物质,宇宙常数的研究可能有重要意义,因此我们研究了共形引力中的球对称时空的场方程,将其转换为Heun方程并讨论了其解。除此之外,我们分别研究了Kerr-Newman时空以及Grumiller时空中的场方程。我们得到,这两种时空中的径向方程也能转换为Heun方程。第五章,总结与展望。最后,在附录中,我们给出了Strum定理,可以利用此定理对事件视界进行分类并得到具体的限制条件。
[Abstract]:This paper is divided into five chapters: chapter 1, we introduce the concept of black hole perturbation and its development. In chapter 2, we first introduce the singularities and solutions of Fuchs type equations where all singularities are regular singularities. Singularities can be divided into removable singularities, poles and natural singularities. Regular singularities are only a special case of poles. Secondly, we discuss the solutions of special differential equations such as Heun equation and confluence Heun equation. When the initial conditions are given, the coefficients of the series solution satisfy a recurrence relation between three terms, which can always be regarded as an expansion of a tridiagonal determinant. Therefore, we discuss the characteristics of tridiagonal determinant and the solution of the equation with tridiagonal determinant zero. In chapter 3, we discuss the Newman-Penrose form of the dynamical equation of spin field, give the definition of cursor-like frame, and obtain the equation of spin coefficient and the equation of field. The Newman-Penrose form is used to study the field equation of general spherically symmetric spacetime. The field equation is divided into radial part and angular part. The solution of angular part is spin weighted spherical harmonic function. According to the singularity, the radial equation can be divided into different cases. We transform the radial equation into some special differential equations, such as the hypergeometric equation Heun equation and the confluence Heun equation, and discuss its solution. In chapter 4, we study the field equations in three special spatiotemporal backgrounds. Because the conformal gravitational field may be of great significance to the study of renormalization, dark matter and cosmic constants, we have studied the field equation of spherical symmetric spacetime in conformal gravity, converted it into Heun equation and discussed its solution. In addition, we study the field equations in Kerr-Newman spacetime and Grumiller spacetime respectively. We have obtained that the radial equation in these two space-time can also be transformed into Heun equation. Chapter five, summary and prospect. Finally, in the appendix, we give the Strum theorem, which can be used to classify the event horizon and obtain the specific limiting conditions.
【学位授予单位】：浙江工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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