【作者】 宋宇；

【导师】 岳瑞宏；

【作者基本信息】 西北大学 ， 理论物理， 2018， 博士

【摘要】 彭罗斯的宇宙监督假设从提出距今已有半个世纪。但至今它仍然是广义相对论尚未解决的开放性问题之一。根据彭罗斯的宇宙监督假设,任何由于引力坍缩产生的奇点都必须被事件视界所隐藏,这暗示了在我们的宇宙中不可能找到裸奇点。检验宇宙监督假设的正确性是广义相对论研究的一个重要的问题。1974年,Wald提出了一个检测宇宙监督假设的理想实验。假设一个观测者从无穷远处向黑洞投入一个测试粒子,如果黑洞吸收了这个粒子后引起事件视界消失,则远处的观测者就会看到裸奇点,这就意味着弱的宇宙监督假设(WCCC)被违反。利用这种方法,在不考虑测试粒子电磁辐射和粒子对背景影响的情况下,Wald发现极端Kerr-Newman黑洞视界不会被测试粒子破坏。本论文的着眼点之一就是使用Wald提出的测试粒子方法来检验彭罗斯的WCCC的有效性。对于宇宙监督假设,目前研究者普遍认为时空奇点只是经典广义相对论产生的结果,如果我们有一个完备的量子引力理论的话,则裸奇点问题自然就可以迎刃而解。但由于至今还没有一个完备的量子引力理论,所以裸奇点问题仍然是个悬而未解的开放性问题。另一方面,由于越来越多的观测证据表明我们的宇宙被暗能量(DE)和冷暗物质(CDM)所主导,其中暗能量推动着宇宙的加速膨胀,暗能量和冷暗物质问题已成为宇宙学迫切需要解决的两个难题。有研究者认为,一个完备的量子引力理论应该可以解释暗能量和冷暗物质问题。这样广义相对论在局域上需要解决奇性问题,而在大尺度上又要回答暗能量问题。奇性问题和暗能量问题是广义相对论需要解决的两个重要问题。在本论文中,研究暗能量和冷暗物质的相互作用问题是另一个着眼点。我们提出了一种协变的暗能量和冷暗物质相互作用模型来避免在辐射早期由于密度扰动而造成的在大尺度上时空曲率发散的问题。本论文第一章首先从时空奇点的定义谈起,以施瓦西时空为例介绍了坐标奇点和曲率奇点的区别;接着介绍了引力坍缩的概念和塌缩形成的两种终态:黑洞或裸奇点;然后又介绍了奇点定理和宇宙监督假设及其检验;最后我们对标准宇宙学模型和宇宙学线性微扰理论基础作简单介绍。在第二章,我们介绍Wald提出的检测宇宙监督假设的理想实验方法,将测试粒子投入一个黑洞来做WCCC的检验。在本论文第三章中,利用第二章介绍的测试粒子研究WCCC的方法,我们研究了三维的极端和近极端Peldan黑洞和MTZ黑洞在吸收一个测试粒子后,是否会导致WCCC的违反。我们发现,只要测试粒子的电荷和能量都合适时是有可能造成WCCC违反的。并且允许破坏黑洞视界的粒子能量范围很窄,这说明粒子破坏黑洞的能量范围?E是经过精细调节的。在极端和近极端情况下,我们还计算了测试粒子在Peldan黑洞和MTZ黑洞视界外的有效势,并用有效势的分析来说明测试粒子是可以掉入黑洞的。在第四章,我们用测试粒子方法研究了极端和近极端Kerr-Newman-Ad S黑洞的WCCC违反。数值计算表明允许测试粒子破坏黑洞视界的能量范围非常窄,这说明所允许的能破坏黑洞的粒子能量范围?E是经过精细调节的。由于允许测试粒子破坏黑洞视界的能量范围非常地窄,所以将粒子电磁辐射和粒子对背景时空影响考虑进去之后,WCCC仍然有效是有可能的。此外,在极端和近极端情况下,我们计算了测试粒子在Kerr-Newman-Ad S黑洞视界外的有效势,用有效势来说明测试粒子可以掉入黑洞。在第五章,我们提出了一个协变的暗能量和冷暗物质相互作用模型。利用这种模型,我们分析了密度扰动的演化。我们发现这种模型可以避免wd为常数且相互作用项与ρm正比的模型在辐射早期由于密度扰动而造成时空不稳定的问题。此外,我们还分析了在辐射时期占主导的非绝热模式,发现在辐射时期非绝热模式正常增长。最后,我们在第六章对本论文做了总结和展望。更多还原

【Abstract】 It has been almost half a century since cosmic censorship was proposed by Penrose in1969.Cosmic censorship is still one of the most important open questions in classical general relativity.According to the well-known “Cosmic Censorship Conjecture(WCCC)” first proposed by Penrose,all physical singularities due to gravitational collapse are hidden behind an event horizon.Cosmic Censorship Conjecture implies that no naked singularity occurs in our universe.Determining the validity of cosmic censorship is perhaps one of the most outstanding problems in the study of general relativity.One way of testing the Weak Cosmic Censorship Conjecture is to throw a test particle into an existing black hole.If the particle can pass through the horizon and change the parameters of the black hole such that the horizon disappears,then the cosmic censorship conjecture might break down.The seminal work was done by Wald in 1974.By neglecting the self-force and radiative effects,Wald investigated if a test particle could destroy the event horizon of an extremal Kerr-Newman black hole.In this thesis,one of focus is to investigate the violation of the WCCC by using this test particle approximation method.On the one hand,it is believed that when we have a reasonable and complete quantum theory of gravity available,all spacetime singularities,whether naked or those hidden inside black holes,will be resolved away.As of now,it remains an open question if the quantum gravity will remove naked singularities.On the other hand,we are convinced by the increasing observations that the present universe is dominated by the so called dark energy(DE)and cold dark matter(CDM).Dark energy and dark matter have been two of the very important issues in the Research of cosmology.Some people believe that when we have a complete quantum theory of gravity available,we can also solve the problem of the dark energy and dark matter.In this thesis,our research also involves dark energy and cold dark matter interactions.We suggest a new covariant model for the energy-momentum transfer between dark energy and cold dark matter to avoid the instabilities caused by the evolution of density perturbations on the supper-Hubble scale.In this thesis,beginning with the discussion on the spacetime singularities,we talk about the difference between the curvature singularity and the coordinate singularity.Then we discuss a gravitational collapse may lead to two different collapse end states: black hole,naked singularity.Then we introduce the singularity theorems and cosmic censorship conjecture.Finally,we introduce some elements of standard cosmology in a more quantitative sense.Then we introduce cosmological perturbation theory in the metric approach.In chapter 2,we introduce a gedanken experiment proposed by Wald in 1974.This gedanken experiment is a way of testing the weak cosmic censorship.In chapter 3,we follow the spirit of Wald’s gedanken experiment and further discuss whether a Peldan(MTZ)black hole can turn into a naked singularity when it captures charged and spinning massive particle.We find that feeding a test particle into an extremal or near extremal Peldan(MTZ)black hole could lead to a violation of cosmic censorship for the black hole.We find the allowed energy window is narrow,which indicates that the allowed energy window must be finely tuned.We use the effective potential of a test particle outside the event horizon to show that the particle could easily fall into the black hole.In chapter 4,using the same method,we find that feeding a test particle into an extremal or near-extremal Kerr-Newman-Ad S black hole could lead to destroy their event horizon,giving rise to naked singularities.The allowed energy window is also very narrow.The fact that ?E is very small leaves the possibility of radiative and self-force effects considerations to cure the problem of WCCC violation in Kerr-Newman-Ad S spacetime.Finally,we use the effective potential of a test particle outside the event horizon to show that the particle could easily fall into an extremal or near-extremal Kerr-Newman-Ad S black hole.In chapter 5,we suggest a new covariant model for the energy-momentum transfer between DE and CDM.Using the covariant model,we analyze the evolution of density perturbations on the supper-Hubble scale.We find that the instabilities can be avoided in the model with constant wdand interaction proportional to ρm.Furthermore,we analyze the dominant non-adiabatic mode in the radiation era and find that the mode grows regularly.In chapter 6,we give a conclusion and outlook.更多还原