本文選題：漸進平坦時空 + Kerr度量�。� 參考：《北京郵電大學(xué)》2011年碩士論文

【摘要】：當(dāng)大質(zhì)量星體發(fā)生引力塌縮時,會導(dǎo)致時空的奇點,然而奇點總是被事件視界所遮蓋,不能通過任何方式影響事件視界外的觀者。這就是說,在事件視界外部,時空具有良好的因果性。同時,從事件視界外的觀者的角度來看,大質(zhì)量星體塌縮后,留下的唯一客體就是黑洞,而事件視界就是它的表面。 本文主要可以分為兩個部分。第一部分,我們著重強調(diào)類光方向及其類光面在時空幾何結(jié)構(gòu)中的重要作用。黑洞時空的光錐結(jié)構(gòu)與類光面的幾何自然的協(xié)調(diào),通過對類光面的分析,我們可以更容易的把握住時空的對稱性,同時從數(shù)學(xué)的角度上講,類光面的分析也揭示了相對論幾何的豐富解析性質(zhì)。在本文中,我們通過對類光面的分析,給出對引力波及其漸進平坦時空的數(shù)學(xué)理解。我們討論在漸進平坦區(qū)域的光錐的幾何性質(zhì),因為這些光錐上面的類光測地線可以到達類光無窮遠,這個條件的成立,需要對光錐加一定程度的限制。完成這步后,我們探討在類光無窮遠鑲嵌一個標準球面的可能性。為了文章內(nèi)容的完整性,本文給出了類光面分析背后的物理意義,并推導(dǎo)類光面上幾何量的傳播方程,及其用數(shù)學(xué)的語言刻畫類光面的幾何圖像。 在文章第二部份,主要考慮Kerr度量。它是由2個參數(shù)刻畫的一組Einstein場方程的解。黑洞究其本質(zhì)而言,構(gòu)成的元素為時間與空間的概念。到目前為止能描述引力塌縮的結(jié)果的嚴格解只有Kerr度量。從這個角度而言,它是最簡單的能為物理學(xué)準確描述的宏觀客體。源于Kerr度量的重要性,歷史上有很多的研究針對著怎樣從數(shù)學(xué)上刻畫Kerr時空,并且這種數(shù)學(xué)描述不依賴于坐標。這些研究往往導(dǎo)致一些重要的數(shù)學(xué)定理的發(fā)現(xiàn)。這類定理有一個統(tǒng)一的名字一無毛定理。無毛定理的多種證明使得物理學(xué)家堅信：在大質(zhì)量星體塌縮過程結(jié)束后,時空逐漸趨于穩(wěn)定,事件視界外面的解也逐漸趨于Kerr解。本文用新的方法來證明無毛定理(唯一性定理)的一種類型。我們關(guān)注靜態(tài)具有事件視界的黑洞時空解,這類黑洞無旋轉(zhuǎn),并且漸進平坦。我們的結(jié)論是這種時空完全由Schwarzschild解來描繪。
[Abstract]:When the gravity collapses of the mass stars, it will lead to the singularities of time and space. However, the singularities are always covered by the event horizon and can not affect the viewers outside the event horizon in any way. This means that, outside the event horizon, space-time has a good causality. At the same time, from the point of view of the viewer outside the event horizon, the only object left behind after the collapse of the mass stars is the black hole, and the event horizon is its surface. This paper can be divided into two parts. In the first part, we emphasize the important role of the optical-like direction and its light-like surface in the geometric structure of time and space. The conical structure of black hole space-time is in harmony with the geometric nature of light-like surface. By analyzing the light-like surface, we can grasp the symmetry of space-time more easily, and at the same time, from a mathematical point of view, The analysis of light-like surfaces also reveals the rich analytical properties of relativistic geometry. In this paper, we give a mathematical understanding of gravitational waves and their asymptotically flat spacetime through the analysis of photo-like surfaces. We discuss the geometric properties of optical cones in an asymptotically flat region, because the quasi-optical geodesic lines above these optical cones can reach the quasi-light infinity. This condition needs to be limited to a certain extent. After completing this step, we explore the possibility of embedding a standard sphere in a similar light infinity. In order to complete the content of the paper, this paper gives the physical meaning behind the light-like surface analysis, and deduces the propagation equation of the geometric quantity on the light-like surface, and describes the geometric image of the light-like surface with mathematical language. In the second part of the article, we mainly consider the Kerr metric. It is the solution of a set of Einstein field equations characterized by two parameters. Black holes are essentially the concepts of time and space. The only strict solution to the result of gravitational collapse so far is the Kerr metric. In this sense, it is the simplest macro object that can be accurately described for physics. Due to the importance of Kerr metrics, there have been many studies on how to describe Kerr spacetime mathematically, and this mathematical description does not depend on coordinates. These studies often lead to the discovery of important mathematical theorems. Such theorems have a uniform name, a hairless theorem. Various proofs of the no-Mao theorem make physicists firmly believe that after the collapse process of the massive stars, the space-time becomes stable gradually, and the solutions outside the event horizon tend to the Kerr solution. In this paper, a new method is used to prove a type of wordless theorem (uniqueness theorem). We focus on spatiotemporal solutions of black holes with event horizon, which are non-rotating and asymptotically flat. Our conclusion is that this time and space is completely described by the Schwarzschild solution.
【學(xué)位授予單位】：北京郵電大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2011
【分類號】：P145.8

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