黑洞与奇点（英文）

黑洞可以说是引力最极端的体现,其视界内是个连光也逃不出去的时空区域。近来黑洞在天文观测方面取得令人惊讶的发展,这其中包括:黑洞碰撞的引力波探测以及M87星系的超大质量黑洞的所谓第一张黑洞照片。但是在理论的层面上,黑洞物理尚有许多未解之谜。其中,信息遗失的悖论是最有名的。但是,有另一个问题至少和信息的丢失一样–甚至更加–令人费解的,就是黑洞内部的奇点性质。时空奇点是广义相对论本身无法描述的,在那里究竟发生什么事?黑洞内部的奇点和宇宙大爆炸时的奇点有何不同?奇点是否会裸露在黑洞外面?所谓"宇宙监督猜想"的假设目前有何进展?我们在这篇半科普的文章中简单的介绍这些课题,希望本文章对物理和数学的本科生有所帮助。     

黑洞的特征声音

正黑洞是时空中的一个区域,任何东西都不能从这个区域里面跑出来。跑不出来的原因,是因为这一区域存在极强的引力,即使是宇宙中跑得最快的光,也逃脱不了其吸引,这使得该区域在光学上是不可见的,所以称之为黑洞。形象地讲,黑洞像是空气中一个不透明的气泡。气泡的边缘,是黑洞的视界;视界之内,外部是看不见的。与气泡不同的是,黑洞内部存在奇点,接近奇点处,引力变得无限大,人们熟知的物理理论在这里失效。对黑洞更深入的理解,是当今理论     

能看清黑洞细节的太空射电望远镜

 能看清黑洞细节的太空射电望远镜俄罗斯科学家试图揭开遥远太空天体---黑洞最神秘的面纱,他们建造了一架能观看到宇宙最深处的射电望远镜。众所周知,黑洞是宇宙中最残忍和最无情的“杀人者”,无论是行星还是恒星在黑洞面前都没有生路。黑洞惊人的吸引力即使是太阳光也无法抗拒,黑洞就像飓风,它会将整个世界吸入风洞中。关于这毁灭性的威胁暂时很少有人知道,因为谁也没有见到过黑洞,但是俄罗斯科学家找到一种能看到黑洞的方法,准备发射一架太空射电望远镜。它将比现有的望远镜敏锐几千倍。俄罗斯科学院院士尼古拉·卡尔达绍夫指出,“这架太空射电望远镜甚至可以看清黑洞的细节,它将能使我们发现宇宙新的物理规律。     

黑洞、暗物质、反物质及宇宙的未来

一、黑洞 现在已有越来越多的证据证实黑洞的存在,那么黑洞是怎么产生的呢？一是宇宙形成时就产生了一些黑洞,再就是恒星的坍缩产物中有一种是黑洞．大恒星的坍缩产物就是黑洞．现在间接观测和推断的结论是：不仅各大星系中都有黑洞,而且在某些星系中心也都有一个大黑洞． 二、暗物质 所谓暗物质就是不能用光学方法直接探测到的物质．理论上认为,暗物质本身既不发光,又不与光发生作用（比如,它不反射光）,只存在万有引力．按现有的天体物理理论计算暗物质占整个宇宙质量的９０％．而我们能观测到的各星系质量仅占整个宇宙质量的１０…     

黑洞的吸积过程

 黑洞是由一个被称为视界的闭合边界所规定的时空区域.这个区域内的引力场是如此之强,以至于没有任何物质能从中逃逸,连光也不例外.也就是说,外部观测者不可能获得视界以内的任何信息.这使得黑洞成为宇宙中最神秘的天体.     

Kerr-Newman-de Sitter黑洞辐射谱和熵修正

本文延拓Damour-Ruffini方法,研究Kerr-Newman-de Sitter黑洞的Hawking辐射.在保持时空中总能量,总角动量和总电荷守恒的条件下,考虑辐射粒子对时空的反作用与黑洞事件视界和宇宙视界的相互关联后,得到了黑洞辐射谱.此辐射不再是严格的纯热谱与黑洞事件视界和宇宙视界对应Bekenstein-Hawking熵变有关.研究发现其结果仍然符合幺正性原理.同时给出了黑洞Bekenstein-Hawking熵的修正项.使人们对黑洞热辐射的研究有了进一步的认识.     

Kiselev黑洞的热力学性质和物质吸积特性

本文考虑带有黑洞视界和宇宙视界的Kiselev时空.研究以黑洞视界和宇宙视界为边界的系统的热力学性质.统一地给出了两个系统的热力学第一定律;在黑洞视界半径远小于宇宙视界半径的情况下,近似地计算了通过宇宙视界和黑洞视界的热能.然后,探讨Kiselev时空的物质吸积特性.在吸积能量密度正比于背景能量密度的条件下给出黑洞的吸积率,讨论了黑洞吸积率与暗能量态方程参数的关系.     

Kerr-Newman-de Sitter黑洞辐射谱和熵修正

本文延拓Damour-Ruffini方法,研究Kerr-Newman-de Sitter黑洞的Hawking辐射.在保持时空中总能量,总角动量和总电荷守恒的条件下,考虑辐射粒子对时空的反作用与黑洞事件视界和宇宙视界的相互关联后,得到了黑洞辐射谱.此辐射不再是严格的纯热谱与黑洞事件视界和宇宙视界对应Bekenstein-Hawking熵变有关.研究发现其结果仍然符合幺正性原理. 同时给出了黑洞Bekenstein-Hawking熵的修正项. 使人们对黑洞热辐射的研究有了进一步的认识.     

婴孩宇宙，黑洞的后裔

在这次讲演里,我想谈谈黑洞,和它的后裔──婴孩宇宙.掉进黑洞已成为科学幻想中的恐怖情节.实际上,黑洞可以说是真正的科学事实,而非科学幻想.我将说明,有很好的理由来预言黑洞的存在.观测证据有力地表明,在我们的星系里有若干黑洞,在别的星系里也有. 当然,科学幻想作家们最感兴趣的是:假如你掉进黑洞,将会发生什么.通常的设想是,黑洞在旋转,你可以穿过时空中的一个小孔,然后到达宇宙的另一区域.显然这增加了太空旅行的可能性.的确,我们需要这样的好事情,即在将来能够实现到别的星球(姑且不谈别的星系)旅行.否则,没有任何东西跑得比光快的事…     

奇点与奇点定理简介（上）

什么是奇点广义相对论中的奇点是一个重要的研究课题,它既是能量条件最早的应用之一,也是全局方法在广义相对论中初试锋芒的范例。我们在《能量条件简介》中曾经提到,广义相对论的经典解(比如施瓦西解)存在奇异性。其中有的奇异性(比如r=2m)可通过坐标变换予以消除,因而不代表物理上的奇点;而有的奇异性(比如r=0)则是真正的物理奇点。很明显,在奇点研究中,真正的物理奇点才是我们感兴趣的对象。那么究竟什么是广义相对论中真正的物理奇点(简称奇点)呢?这初看似乎是一个很简单的问题。奇点显然就是那些时空结构具有某种病态性质的时空点。但…     

Observers in Kerr spacetimes: the ergoregion on the equatorial plane

We perform a detailed analysis of the properties of stationary observers located on the equatorial plane of the ergosphere in a Kerr spacetime, including light-surfaces. This study highlights crucial differences between black hole and the super-spinner sources. In the case of Kerr naked singularities, the results allow us to distinguish between “weak” and “strong ” singularities, corresponding to spin values close to or distant from the limiting case of extreme black holes, respectively. We derive important limiting angular frequencies for naked singularities. We especially study very weak singularities as resulting from the spin variation of black holes. We also explore the main properties of zero angular momentum observers for different classes of black hole and naked singularity spacetimes.     

Astrophysical Black Holes as Natural Laboratories for Fundamental Physics and Strong-Field Gravity

Astrophysical tests of general relativity belong to two categories: 1) “internal”, i.e. consistency tests within the theory (for example, tests that astrophysical black holes are indeed described by the Kerr solution and its perturbations), or 2) “external”, i.e. tests of the many proposed extensions of the theory. I review some ways in which astrophysical black holes can be used as natural laboratories for both “internal” and “external” tests of general relativity. The examples provided here (ringdown tests of the black hole “no-hair” theorem, bosonic superradiant instabilities in rotating black holes and gravitational-wave tests of massive scalar-tensor theories) are shamelessly biased towards recent research by myself and my collaborators. Hopefully this colloquial introduction aimed mainly at astrophysicists will convince skeptics (if there are any) that space-based detectors will be crucial to study fundamental physics through gravitational-wave observations.     

Black hole bombs and explosions: from astrophysics to particle physics

Black holes are the elementary particles of gravity, the final state of sufficiently massive stars and of energetic collisions. With a 40-year long history, black hole physics is a fully-blossomed field which promises to embrace several branches of theoretical physics. Here I review the main developments in highly dynamical black holes with an emphasis on high energy black hole collisions and probes of particle physics via superradiance. This write-up, rather than being a collection of well known results, is intended to highlight open issues and the most intriguing results.     

Exact self-gravitating N-body motion in the CGHS model

In the asymptotically flat two-dimensional dilaton gravity, we present an N-body particle action which has a dilaton coupled mass term for the exact solubility. This gives nonperturbative exact solutions for the N-body self-gravitating system, so the infalling particles form a black hole and their trajectories are exactly described. In our two-dimensional case, the critical mass for the formation of black holes does not exist, so even a single particle forms a black hole. The infalling particles give additional time-like singularities in addition to the space-like black hole singularity. However, the latter singularities can be properly cloaked by the future horizons within some conditions.     

Exact self-gravitating N-body motion in the CGHS model

In the asymptotically flat two-dimensional dilaton gravity, we present an N-body particle action which has a dilaton coupled mass term for the exact solubility. This gives nonperturbative exact solutions for the N-body self-gravitating system, so the infalling particles form a black hole and their trajectories are exactly described. In our two-dimensional case, the critical mass for the formation of black holes does not exist, so even a single particle forms a black hole. The infalling particles give additional time-like singularities in addition to the space-like black hole singularity. However, the latter singularities can be properly cloaked by the future horizons within some conditions.     

Black hole and hawking radiation by type-II Weyl fermions

The type-II Weyl and type-II Dirac fermions may emerge behind the event horizon of black holes. Correspondingly, the black hole can be simulated by creation of the region with overtilted Weyl or Dirac cones. The filling of the electronic states inside the “black hole” is accompanied by Hawking radiation. The Hawking temperature in the Weyl semimetals can reach the room temperature, if the black hole region is sufficiently small, and thus the effective gravity at the horizon is large.     

Complexity growth rates for AdS black holes in massive gravity and <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The “complexity = action” duality states that the quantum complexity is equal to the action of the stationary AdS black hole within the Wheeler–DeWitt patch at late time approximation. We compute the action growth rates of the neutral and charged black holes in massive gravity and the neutral, charged and Kerr–Newman black holes in f(R) gravity to test this conjecture. Besides, we investigate the effects of the massive graviton terms, higher derivative terms and the topology of the black hole horizon on the complexity growth rate.     

Difficulties of quantitative tests of the Kerr-hypothesis with X-ray observations of mass accreting black holes

X-ray studies of stellar mass black holes in X-ray binaries and mass-accreting supermassive black holes in Active Galactic Nuclei have achieved a high degree of maturity and have delivered detailed information about the astrophysical sources and the physics of black hole accretion. In this article, I review recent progress made towards using the X-ray observations for testing the “Kerr hypothesis” that the background spacetimes of all astrophysical quasi-stationary black holes are described by the Kerr metric. Although the observations have indeed revealed clear evidence for relativistic effects in strong-field gravity, quantitative tests of the Kerr hypothesis still struggle with theoretical and practical difficulties. In this article, I describe several recently introduced test metrics and review the status of constraining the background spacetimes of mass accreting stellar mass and supermassive black holes with these test metrics. The main conclusion of the discussion is that astrophysical uncertainties are large compared to the rather small observational differences between the Kerr and non-Kerr metrics precluding quantitative constraints on deviations from the Kerr metric at this point in time. I conclude with discussing future progress enabled by more detailed numerical simulations and by future X-ray spectroscopy, timing, polarimetry, and interferometry missions.     

Direct imaging rapidly-rotating non-Kerr black holes

Recently, two of us have argued that non-Kerr black holes in gravity theories different from General Relativity may have a topologically non-trivial event horizon. More precisely, the spatial topology of the horizon of non-rotating and slow-rotating objects would be a 2-sphere, like in Kerr space–time, while it would change above a critical value of the spin parameter. When the topology of the horizon changes, the black hole central singularity shows up. The accretion process from a thin disk can potentially overspin these black holes and induce the topology transition, violating the Weak Cosmic Censorship Conjecture. If the astrophysical black hole candidates are not the black holes predicted by General Relativity, we might have the quite unique opportunity to see their central region, where classical physics breaks down and quantum gravity effects should appear. Even if the quantum gravity region turned out to be extremely small, at the level of the Planck scale, the size of its apparent image would be finite and potentially observable with future facilities.     

Black holes in general relativity

It is assumed that the singularities which occur in gravitational collapse are not visible from outside but are hidden behind an event horizon. This means that one can still predict the future outside the event horizon. A black hole on a spacelike surface is defined to be a connected component of the region of the surface bounded by the event horizon. As time increase, black holes may merge together but can never bifurcate. A black hole would be expected to settle down to a stationary state. It is shown that a stationary black hole must have topologically spherical boundary and must be axisymmetric if it is rotating. These results together with those of Israel and Carter go most of the way towards establishing the conjecture that any stationary black hole is a Kerr solution. Using this conjecture and the result that the surface area of black holes can never decrease, one can place certain limits on the amount of energy that can be extracted from black holes.