弯曲时空中试验粒子的动力学研究

发布时间：2018-05-20 13:34

本文选题：测地线 + 弯曲时空　；参考：《湖南师范大学》2016年博士论文

【摘要】：广义相对论中,测地线的概念将“直线”推广到弯曲时空,任何不受除引力之外的其他力作用的自由粒子的世界线就是一条典型的测地线。即自由移动或下落的粒子都将沿测地线运动。引力在广义相对论的观点看来不是一种力的作用,而是时空几何弯曲的结果,弯曲时空的源头是能动张量,例如物质。因此,恒星周围一颗行星的运动轨道是四维弯曲时空中恒星周围的一条测地线在三维空间中的投影。天体物理学家在研究黑洞的吸积盘模型时常常近似地假定被吸积物质沿测地线运动,认为黑洞附近的辐射沿类光测地线进入奇点或传向远方观测者。了解黑洞的时空几何性质的最好的方法是研究其类时和类光测地线。本文通过分析不同黑洞时空中的试验粒子或光子的有效势,找出对应能量的粒子的所有可能测地线轨道类型,并通过解测地线方程,求出粒子运动轨道数值解,直观地描绘出粒子具体的运动轨道图像,展示了所研究的黑洞时空几何性质。第二章我们具体讨论了一个膜理论中的球对称黑洞外部精确解,其可用来解释星系旋转曲线而无需假定暗物质的存在。我们用分析试验粒子有效势的方法研究了在此球对称黑洞时空中的类时测地线结构,详细地考虑了宇宙常数参数α和恒星压力参数β对黑洞类时测地线结构影响。通过分析我们发现试验粒子的初始条件和能量决定了其多种运动情况：试验粒子在束缚轨道上运动；试验粒子在稳定或不稳定的圆形轨道上运动；试验粒子处于陷入奇点或飞向无穷远处的逃逸轨道等等情形。通过比较粒子在恒星压力参数口和宇宙常数参数a取不同值时的有效势曲线,我们发现恒星压力参数β不影响黑洞的类时测地线结构,但宇宙常数参数α影响黑洞的类时测地线结构。在本文的第三章中,我们研究了Bardeen时空中类时和类光测地线结构。Bardeen时空描述一个非奇异性的时空,即一个无奇点的黑洞时空。通过分析粒子和光子有效势曲线,我们根据对应有效势曲线的能量值数值计算出了所有可能存在的具体轨道。我们在这个时空中找到了多世界束缚轨道,两世界逃逸轨道,这种类型是史瓦西黑洞中不存在的。我们也发现两种束缚轨道的进动方向相反以及它们的进动速度不同,穿越视界的束缚轨道进动速度较快,但视界外面的束缚轨道进动速度较慢。第四章中研究了Janis-Newman- Winicour(JNW)时空的测地线结构,JNW度规由史瓦西度规发展而来,我们将度规中的参数μ分为三个区间,当μ处于不同区间时,其对应的测地线结构有着根本的区别。我们详细讨论了参数μ分别处于这三个区间时有效势曲线的行为和对应能量的试验粒子的所有测地线类型。
[Abstract]:In general relativity, the concept of geodesic line extends "straight line" to curved spacetime. The world line of any free particle which is not subjected to any force other than gravity is a typical geodesic line. That is, particles that move freely or fall will move along geodesic lines. From the viewpoint of general relativity, gravity is not a force, but a result of geometric bending of spacetime. The source of bending spacetime is active Zhang Liang, such as matter. Therefore, the orbit of a planet around a star is the projection of a geodesic line around a star in four dimensional curved spacetime in three dimensional space. In studying accretion disk models of black holes astrophysicists often approximately assume that accreted matter moves along geodesic lines and considers that radiation near black holes enters singularities or propagates to distant observers along photogeodesic lines. The best way to understand the space-time geometric properties of black holes is to study their time-like and photogeodesic properties. In this paper, by analyzing the effective potential of experimental particles or photons in different black hole space-time, we find out all the possible geodesic orbital types of particles corresponding to the corresponding energy, and solve the geodesic equation to obtain the numerical solution of the motion orbit of the particles. The moving orbit images of particles are depicted intuitively and the space-time geometric properties of black holes studied are shown. In chapter 2, we discuss the exact solution of a spherically symmetric black hole in film theory, which can be used to explain the rotation curve of galaxies without assuming the existence of dark matter. The time-like geodesic structure in the space-time of the spherically symmetric black hole is studied by using the method of analyzing the experimental particle effective potential. The effects of the cosmic constant parameter 伪 and the star pressure parameter 尾 on the time-like geodesic structure of the black hole are considered in detail. Through the analysis, we find that the initial conditions and energy of the test particle determine its motion: the test particle moves on the bound orbit, the test particle moves on the stable or unstable circular orbit, and the experimental particle moves on the stable or unstable circular orbit. The test particles are trapped in singularities or in flight orbits to infinity, and so on. By comparing the effective potential curves of particles with different values of stellar pressure parameters and cosmic constant parameters a, we find that star pressure parameters 尾 do not affect the time-like geodesic structure of black holes. But the cosmic constant parameter 伪 affects the time-like geodesic structure of black hole. In the third chapter of this paper, we study the time-like and photonic geodesic structure in Bardeen spacetime. Bardeen space-time describes a non-singular space-time, that is, a black hole spacetime without singularities. By analyzing the effective potential curves of particles and photons, we calculate all possible orbits according to the energy values of the corresponding effective potential curves. We found the multiworld bound orbit and the two-world escape orbit in this spacetime, which is a type that is not present in the Schwarzie black hole. We also find that the precession direction of the two kinds of bound orbits is opposite and their precession velocities are different. The precession speed of the bound orbits passing through the horizon is faster but that of the bound orbits outside the horizon is slower. In chapter 4, the geodesic structure of Janis-Newman-Winicouror JNW) is studied. The geodesic structure of Janis-Newman-Winicouror JNW) is derived from the Swarthy metric. The parameter 渭 in the metric is divided into three intervals. When 渭 is in different intervals, the geodesic structure of the geodesic structure is fundamentally different. We discuss in detail the behavior of the effective potential curve and all geodesic types of the test particles corresponding to the energy when the parameter 渭 is in these three regions respectively.
【学位授予单位】：湖南师范大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：P145.8

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