本文關(guān)鍵詞：旋轉(zhuǎn)壓縮視界Kaluza-Klein黑洞時(shí)空中的強(qiáng)引力透鏡　出處：《湖南師范大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

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【摘要】：廣義相對(duì)論指出物質(zhì)及其運(yùn)動(dòng)將導(dǎo)致時(shí)空的彎曲從而使得經(jīng)過其附近的光線發(fā)生偏轉(zhuǎn),這就是引力透鏡效應(yīng)。引力透鏡效應(yīng)被廣泛應(yīng)用于暗物質(zhì)分布的探測(cè),宇宙常數(shù)的限定,遙遠(yuǎn)暗淡星體的觀測(cè)等諸多領(lǐng)域,也可用于檢驗(yàn)和鑒別廣義相對(duì)論和高維弦理論等各種引力理論。強(qiáng)引力透鏡效應(yīng)是指光線經(jīng)過強(qiáng)引力場(chǎng)發(fā)生大角度偏轉(zhuǎn)的現(xiàn)象。當(dāng)光線經(jīng)過光球半徑附近時(shí),它可以繞透鏡天體若干圈再出射形成相對(duì)論像；在理論上黑洞的兩側(cè)可產(chǎn)生無(wú)窮多個(gè)相對(duì)論像；通過觀測(cè)這些像的角位置與相對(duì)亮度,可以推斷中心天體的結(jié)構(gòu)和時(shí)空參數(shù)。本文將對(duì)旋轉(zhuǎn)壓縮視界Kaluza-Klein (KK)黑洞時(shí)空中的強(qiáng)引力透鏡現(xiàn)象進(jìn)行研究。在第一章,我們對(duì)引力透鏡的基本原理,分類,和應(yīng)用進(jìn)行簡(jiǎn)單介紹；并介紹計(jì)算偏轉(zhuǎn)角,放大率及成像位置的基本公式。在第二章,我們將介紹V.Bozza研究球?qū)ΨQ靜態(tài)黑洞時(shí)空中強(qiáng)引力透鏡問題所提出的偏轉(zhuǎn)角公式。V.Bozza的工作表明,當(dāng)光線的徑向坐標(biāo)駐點(diǎn)x0不斷趨近光球半徑xm時(shí),光線偏轉(zhuǎn)角呈對(duì)數(shù)增長(zhǎng),最終趨于發(fā)散。利用強(qiáng)場(chǎng)近似方法,V.Bozza建立起了度規(guī)參數(shù)與強(qiáng)引力透鏡的各觀測(cè)量之間的聯(lián)系,為通過對(duì)強(qiáng)引力透鏡現(xiàn)象的觀測(cè)來推斷透鏡天體的時(shí)空結(jié)構(gòu)提供了理論依據(jù)。在第三章,我們應(yīng)用V.Bozza的方法,研究了旋轉(zhuǎn)壓縮視界Kaluza-Klein黑洞時(shí)空中的強(qiáng)引力透鏡效應(yīng),并與四維Kerr黑洞時(shí)空以及Godel壓縮視界KK黑洞時(shí)空中的強(qiáng)引力透鏡效應(yīng)做了對(duì)比,總結(jié)這些不同類型的旋轉(zhuǎn)參數(shù)對(duì)黑洞強(qiáng)引力透鏡的影響。我們發(fā)現(xiàn)：(1)在旋轉(zhuǎn)壓縮視界KK黑洞時(shí)空中,光球半徑腦,強(qiáng)引力透鏡偏轉(zhuǎn)角公式中的系數(shù)a,b,φ方向的偏轉(zhuǎn)角a(θ),以及相應(yīng)的觀測(cè)量與光線在赤道面上的繞行方向無(wú)關(guān)。Godel壓縮視界KK黑洞時(shí)空中的強(qiáng)引力透鏡效應(yīng)也具有相似的性質(zhì)。這是壓縮視界KK黑洞時(shí)空強(qiáng)引力透鏡效應(yīng)與Kerr旋轉(zhuǎn)黑洞時(shí)空中強(qiáng)引力透鏡效應(yīng)一個(gè)截然不同的性質(zhì)。(2)旋轉(zhuǎn)壓縮視界KK黑洞時(shí)空中,當(dāng)旋轉(zhuǎn)參數(shù)b固定時(shí),光球半徑ρps及相應(yīng)的像的角位置θ∞隨額外維尺度ρ0的增加先減小后增加。而在Godel壓縮視界KK黑洞中,當(dāng)旋轉(zhuǎn)參數(shù)j較小時(shí),光球半徑ρps及相應(yīng)的像的角位置θ∞隨額外維尺度ρ0增加單調(diào)遞增；當(dāng)旋轉(zhuǎn)參數(shù)j較大時(shí),則這些量隨之遞減。(3)在極限壓縮情形ρ0=0下,旋轉(zhuǎn)壓縮視界KK黑洞時(shí)空中的強(qiáng)引力透鏡偏轉(zhuǎn)角公式系數(shù)a隨旋轉(zhuǎn)參數(shù)單調(diào)增加,而在Godel壓縮視界KK黑洞時(shí)空中,它則是一個(gè)不隨旋轉(zhuǎn)參數(shù)變化的常數(shù)。最后,我們對(duì)旋轉(zhuǎn)壓縮視界KK黑洞時(shí)空的強(qiáng)引力透鏡效應(yīng)的研究進(jìn)行了總結(jié)和對(duì)將來的研究做了一些展望。
[Abstract]:The general theory of relativity points out that matter and its motion will cause the curvature of space and time to deflect the light passing through its vicinity, which is called gravitational lensing effect, which is widely used in the detection of dark matter distribution. The limitation of cosmic constant, the observation of distant dim stars and so on. It can also be used to test and distinguish various gravitational theories such as general relativity theory and high dimensional string theory. Strong gravitational lensing effect refers to the phenomenon of large angle deflection of light through strong gravitational field. It can circle the lens object several times and then shoot out to form a relativistic image. Theoretically, an infinite number of relativistic images can be produced on both sides of a black hole. By observing the angular position and relative brightness of these images. The structure and space-time parameters of the central celestial body can be inferred. In this paper, the phenomenon of strong gravitational lensing in the spacetime of the Kaluza-Klein KK black hole at the event horizon of rotation compression is studied. The basic principle, classification and application of gravitational lensing are briefly introduced. The basic formulas for calculating deflection angle, magnification and imaging position are also introduced in chapter 2. We will introduce V. Bozza's work on the deflection angle formula of V. Bozza for studying the problem of strong gravitational lensing in space-time of spherically symmetric static black hole. When the radial coordinates of the ray stationary point x0 keep approaching the radius of the light sphere x m, the deflection angle of the light increases logarithm and eventually tends to diverge. The strong field approximation method is used. V.Bozza has established a relationship between the metric parameters and the observations of a strong gravitational lens. This paper provides a theoretical basis for inferring the space-time structure of lens objects by observing the phenomena of strong gravitational lensing. In Chapter 3, we apply V. Bozza's method. The strong gravitational lensing effect in the spacetime of Kaluza-Klein black hole at the event horizon of rotation compression is studied. The results are compared with the strong gravitational lensing effect in four-dimensional Kerr black hole spacetime and Godel squeezed KK black hole spacetime. In this paper, we summarize the effect of these kinds of rotation parameters on the strong gravitational lensing of black hole. We find that the coefficient a in the formula of deflection angle of strong gravitational lens in the space and time of KK black hole at the event horizon of rotation compression is the radius of light sphere brain and the deflection angle of strong gravitational lens. The deflection angle a (胃) in the direction of b, 蠁. The strong gravitational lensing effect in the spacetime of the KK black hole at the event horizon of Godel squeezing has similar properties. This is the strong space-time property of the squeezed horizon KK black hole. The gravitational lensing effect is a very different property from the strong gravitational lensing effect in the spacetime of Kerr rotating black hole. 2) the space time of the KK black hole at the event horizon of rotation compression. When the rotation parameter b is fixed, the radius 蟻 PS and the angular position 胃 鈭，

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