【摘要】：黑洞是廣義相對(duì)論最偉大的預(yù)言之一。然而,黑洞存在許多不可思議的物理現(xiàn)象,其中最為人所知的是黑洞的中央奇點(diǎn)的存在。當(dāng)奇點(diǎn)存在時(shí)物理定律在這里失效,但是根據(jù)現(xiàn)有的廣義相對(duì)論理論,存在奇點(diǎn)的黑洞解又是不可避免的,例如史瓦西黑洞,R-N黑洞和Kerr黑洞等。在廣義相對(duì)論中,尋找中心不存在奇點(diǎn)的黑洞的問題是非常重要的。因此,一些量子模型和幾何的模型來克服奇點(diǎn)的問題。其中后一種將是我們這里要討論的理論模型,它以Bardeen黑洞為代表。為了研究隱藏在視界后面的黑洞的性質(zhì),對(duì)黑洞時(shí)空作擾動(dòng)是不錯(cuò)的了解視角。通過視界的擾動(dòng)會(huì)產(chǎn)生一些物理現(xiàn)象,其中包括了我們這里要研究的擬正則模,從而我們能分析黑洞在擾動(dòng)下的穩(wěn)定性。黑洞的擬正則模是復(fù)數(shù),它攜帶了黑洞在擾動(dòng)后如何恢復(fù)穩(wěn)定的信息,它的數(shù)值與黑洞時(shí)空的性質(zhì)和擾動(dòng)的類型有關(guān)。本文研究帶有de Sitter中心的球?qū)ΨQ黑洞在標(biāo)量場(chǎng)擾動(dòng)下的擬正則模。幾何上來講,這種黑洞在半徑很大的時(shí)候趨近與史瓦西解形式,在趨于0的時(shí)候是de Sitter解形式的。在這里我們通過變化參數(shù)(它與宇宙學(xué)常數(shù)有關(guān)),角量子數(shù),泛音數(shù)和黑洞質(zhì)量來研究這個(gè)黑洞的擬正則模。根據(jù)6階WKB近似的計(jì)算結(jié)果,我們發(fā)現(xiàn)擬正則模在隨的變化出現(xiàn)極大值和極小值,同時(shí)對(duì)于一定范圍的,當(dāng)擬正則模隨泛音數(shù)n變化時(shí)也會(huì)出現(xiàn)極值現(xiàn)象,這是值得關(guān)注的。這個(gè)愛因斯坦方程的精確解析解不帶電,沒有用到電動(dòng)力學(xué)或其他的理論,所以通過對(duì)真空無奇點(diǎn)黑洞的擬正則模的研究,將有助于我們對(duì)不帶電的無奇點(diǎn)黑洞的性質(zhì)的了解。
[Abstract]:Black holes are one of the greatest prophecies of general relativity. However, black holes have many incredible physical phenomena, among which the existence of central singularities of black holes is best known. When the singularity exists, the laws of physics fail here, but according to the existing theory of general relativity, the solution of the black hole with singularity is inevitable, such as the Schwarzie black hole, R-N black hole and Kerr black hole, etc. In general relativity, the problem of finding black holes with no singularities in the center is very important. Therefore, some quantum models and geometric models to overcome the singularity problem. The latter will be the theoretical model we will discuss here, as represented by the Bardeen black hole. In order to study the properties of black holes hidden behind the event horizon, it is a good way to understand the space-time perturbation of black holes. Some physical phenomena can be generated by the perturbation of the event horizon, including the quasi-regular modes that we are going to study here, so that we can analyze the stability of black holes under perturbation. The quasi-regular mode of a black hole is a complex number, which carries information on how the black hole recovers stability after disturbance. Its numerical value is related to the properties of the space-time and the type of perturbation of the black hole. In this paper, the quasi-regular modes of a spherically symmetric black hole with de Sitter center under scalar field perturbation are studied. Geometrically, the black hole approaches to the Schwarzie solution form when its radius is very large, and is de Sitter solution form when it tends to 0. Here we study the quasi-regular modes of the black hole by varying the parameters (which are related to cosmological constants), angular quantum numbers, generalized sound numbers, and the mass of the black hole. According to the results of the WKB approximation of order 6, we find that the maximum and minimum value of quasi-regular modules appear with the change of the number of overtones n, and for a certain range, the phenomenon of extreme values will also appear when the quasi-regular modules change with the number of overtones n, which is worthy of attention. The exact analytical solution of this Einstein equation is not charged and does not use electrodynamics or other theories. Therefore, the study of quasi-regular modes of a vacuum black hole without singularities will help us to understand the properties of an uncharged black hole without singularities.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：P145.8

【參考文獻(xiàn)】

相關(guān)碩士學(xué)位論文 前1條

1 楊彬;漸近安全引力中黑洞的擬正則模[D];上海師范大學(xué);2012年

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本文編號(hào)：2384401