本文選題：測地線 + 彎曲時(shí)空��； 參考：《湖南師范大學(xué)》2016年博士論文

【摘要】：廣義相對(duì)論中,測地線的概念將“直線”推廣到彎曲時(shí)空,任何不受除引力之外的其他力作用的自由粒子的世界線就是一條典型的測地線。即自由移動(dòng)或下落的粒子都將沿測地線運(yùn)動(dòng)。引力在廣義相對(duì)論的觀點(diǎn)看來不是一種力的作用,而是時(shí)空幾何彎曲的結(jié)果,彎曲時(shí)空的源頭是能動(dòng)張量,例如物質(zhì)。因此,恒星周圍一顆行星的運(yùn)動(dòng)軌道是四維彎曲時(shí)空中恒星周圍的一條測地線在三維空間中的投影。天體物理學(xué)家在研究黑洞的吸積盤模型時(shí)常常近似地假定被吸積物質(zhì)沿測地線運(yùn)動(dòng),認(rèn)為黑洞附近的輻射沿類光測地線進(jìn)入奇點(diǎn)或傳向遠(yuǎn)方觀測者。了解黑洞的時(shí)空幾何性質(zhì)的最好的方法是研究其類時(shí)和類光測地線。本文通過分析不同黑洞時(shí)空中的試驗(yàn)粒子或光子的有效勢,找出對(duì)應(yīng)能量的粒子的所有可能測地線軌道類型,并通過解測地線方程,求出粒子運(yùn)動(dòng)軌道數(shù)值解,直觀地描繪出粒子具體的運(yùn)動(dòng)軌道圖像,展示了所研究的黑洞時(shí)空幾何性質(zhì)。第二章我們具體討論了一個(gè)膜理論中的球?qū)ΨQ黑洞外部精確解,其可用來解釋星系旋轉(zhuǎn)曲線而無需假定暗物質(zhì)的存在。我們用分析試驗(yàn)粒子有效勢的方法研究了在此球?qū)ΨQ黑洞時(shí)空中的類時(shí)測地線結(jié)構(gòu),詳細(xì)地考慮了宇宙常數(shù)參數(shù)α和恒星壓力參數(shù)β對(duì)黑洞類時(shí)測地線結(jié)構(gòu)影響。通過分析我們發(fā)現(xiàn)試驗(yàn)粒子的初始條件和能量決定了其多種運(yùn)動(dòng)情況：試驗(yàn)粒子在束縛軌道上運(yùn)動(dòng)；試驗(yàn)粒子在穩(wěn)定或不穩(wěn)定的圓形軌道上運(yùn)動(dòng)；試驗(yàn)粒子處于陷入奇點(diǎn)或飛向無窮遠(yuǎn)處的逃逸軌道等等情形。通過比較粒子在恒星壓力參數(shù)口和宇宙常數(shù)參數(shù)a取不同值時(shí)的有效勢曲線,我們發(fā)現(xiàn)恒星壓力參數(shù)β不影響黑洞的類時(shí)測地線結(jié)構(gòu),但宇宙常數(shù)參數(shù)α影響黑洞的類時(shí)測地線結(jié)構(gòu)。在本文的第三章中,我們研究了Bardeen時(shí)空中類時(shí)和類光測地線結(jié)構(gòu)。Bardeen時(shí)空描述一個(gè)非奇異性的時(shí)空,即一個(gè)無奇點(diǎn)的黑洞時(shí)空。通過分析粒子和光子有效勢曲線,我們根據(jù)對(duì)應(yīng)有效勢曲線的能量值數(shù)值計(jì)算出了所有可能存在的具體軌道。我們?cè)谶@個(gè)時(shí)空中找到了多世界束縛軌道,兩世界逃逸軌道,這種類型是史瓦西黑洞中不存在的。我們也發(fā)現(xiàn)兩種束縛軌道的進(jìn)動(dòng)方向相反以及它們的進(jìn)動(dòng)速度不同,穿越視界的束縛軌道進(jìn)動(dòng)速度較快,但視界外面的束縛軌道進(jìn)動(dòng)速度較慢。第四章中研究了Janis-Newman- Winicour(JNW)時(shí)空的測地線結(jié)構(gòu),JNW度規(guī)由史瓦西度規(guī)發(fā)展而來,我們將度規(guī)中的參數(shù)μ分為三個(gè)區(qū)間,當(dāng)μ處于不同區(qū)間時(shí),其對(duì)應(yīng)的測地線結(jié)構(gòu)有著根本的區(qū)別。我們?cè)敿?xì)討論了參數(shù)μ分別處于這三個(gè)區(qū)間時(shí)有效勢曲線的行為和對(duì)應(yīng)能量的試驗(yàn)粒子的所有測地線類型。
[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 偽 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 偽 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.
【學(xué)位授予單位】：湖南師范大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：P145.8

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