The singularity theorems of Hawking and Penrose tell us that singularities are common place in general relativity. Singularities not only occur at the beginning of the Universe at the Big Bang, but also in complete gravitational collapses that result in the formation of black holes. If singularities - except the one at the Big Bang - ever become "naked", i.e., not shrouded by black hole horizons, then it is expected that problems would arise and render general relativity indeterministic. For this reason, Penrose proposed the cosmic censorship conjecture, which states that singularities should never be naked. Various counterexamples to the conjecture have since been discovered, but it is still not clear under which kind of physical processes one can expect violation of the conjecture. In this short review, I briefly examine some progresses in spacetime singularities and cosmic censorship conjecture. In particular, I shall discuss why we should still care about the conjecture, and whether we should be worried about some of the counterexamples. This is not meant to be a comprehensive review, but rather to give an introduction to the subject, which has recently seen an increase of interest.
We give two new analytical solutions to the low-energy string theory action that violate the weak cosmic censorship conjecture. They are classical charged solutions to the Einstein-Maxwell-dilaton theory in four dimensions that come in two types. The first represents one single naked singularity whose asymptotic region is flat. Its mass respects the positive mass theorem. The absence of horizons allows us to probe quantum aspects of gravity by direct observation of these singularities. The second represents singularities that come in pairs that "seem to create their own spacetime", and the reg…
In analyzing maximally symmetric Lovelock black holes with non-planar horizon topologies, many novel features have been observed. The existence of finite radius singularities, a mass gap in the black hole spectrum and solutions displaying multiple horizons are noteworthy examples. Naively, in all these cases, the appearance of naked singularities seems unavoidable, leading to the question of whether these theories are consistent gravity theories. We address this question and show that whenever the cosmic censorship conjecture is threaten, an instability generically shows up driving the system …
We review the status of the weak cosmic censorship conjecture, which asserts, in essence, that all singularities of gravitational collapse are hidden within black holes. Although little progress has been made toward a general proof (or disproof) of this conjecture, there has been some notable recent progress in the study of some examples and special cases related to the conjecture. These results support the view that naked singularities cannot arise generically.
A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized s…
We present here a brief review and discussion on recent developments in the theory of spacetime singularities. After mentioning some key motivations on the main ideas and concepts involved, we take the approach that the singularities will be eventually resolved by the quantum gravity effects. Some consequences are indicated when such singularities are visible to far away observers in the universe.
This paper is a further development of the approach to weak cosmic censorship proposed by the authors in Ref. 5. We state and prove a modified version of that work's main result under significantly relaxed assumptions on the asymptotic structure of space--time. The result, which imposes strong constraints on the occurrence of naked singularities of the strong curvature type, is in particular applicable to physically realistic cosmological models.
The global structure of 2-dimensional dilaton gravity is studied, attending in particular to black holes and singularities. A gravitational energy is defined and shown to be positive at spatial singularities and negative at temporal singularities. Trapped points are defined, and it is shown that spatial singularities are trapped and temporal singularities are not. Thus a local form of cosmic censorship holds for positive energy. In an analogue of gravitational collapse to a black hole, matter falling into an initially flat space creates a spatial curvature singularity which is cloaked in a spa…
Extending the study of spherically symmetric metrics satisfying the dominant energy condition and exhibiting singularities of power-law type initiated in SI93, we identify two classes of peculiar interest: focusing timelike singularity solutions with the stress-energy tensor of a radiative perfect fluid (equation of state: $p={1\over 3} ρ$) and a set of null singularity classes verifying identical properties. We consider two important applications of these results: to cosmology, as regards the possibility of solving the horizon problem with no need to resort to any inflationary scenario, and t…
We present a new approach to the issues of spacetime singularities and cosmic censorship in general relativity. This is based on the idea that standard 4-dimensional spacetime is the conformal infinity of an ambient metric for the 5-dimensional Einstein equations with fluid sources. We then find that the existence of spacetime singularities in four dimensions is constrained by asymptotic properties of the ambient 5-metric, while the non-degeneracy of the latter crucially depends on cosmic censorship holding on the boundary.
We find asymptotically anti de Sitter solutions in N=8 supergravity which have negative total energy. This is possible since the boundary conditions required for the positive energy theorem are stronger than those required for finite mass (and allowed by string theory). But stability of the anti de Sitter vacuum is still ensured by the positivity of a modified energy, which includes an extra surface term. Some of the negative energy solutions describe classical evolution of nonsingular initial data to naked singularities. Since there is an open set of such solutions, cosmic censorship is viola…
We study the occurrence of naked singularities in the spherically symmetric collapse of radiation shells in a higher dimensional spacetime. The necessary conditions for the formation of a naked singularity or a black hole are obtained. The naked singularities are found to be strong in the Tipler's sense and thus violating cosmic censorship conjecture.
Recently Hertog, Horowitz, and Maeda have argued that cosmic censorship can be generically violated in string theory in anti-de Sitter spacetime by considering a collapsing bubble of a scalar field whose mass saturates the Breitenlohner-Freedman bound. We study this system numerically and find that for various choices of initial data black holes form rather than naked singularities, implying that in these cases cosmic censorship is upheld.
We investigate the occurrence and nature of naked singularities in the gravitational collapse of a self-similar adiabatic perfect fluid in a five dimensional space-time. The naked singularities are found to be gravitationally strong in the sense of Tipler and thus violate the cosmic censorship conjecture.
We explore the cosmic censorship in the Einstein-Maxwell-dilaton theory following Wald's thought experiment to destroy a black hole by throwing in a test particle. We discover that at probe limit the extremal charged dilaton black hole could be destroyed by a test particle with specific energy. Nevertheless the censorship is well protected if backreaction or self-force is included. At the end, we discuss an interesting connection between Hoop Conjecture and Weak Gravity Conjecture.
In the light of his recent (and fully deserved) Nobel Prize, this pedagogical paper draws attention to a fundamental tension that drove Penrose's work on general relativity. His 1965 singularity theorem (for which he got the prize) does not in fact imply the existence of black holes (even if its assumptions are met). Similarly, his versatile definition of a singular space-time does not match the generally accepted definition of a black hole (derived from his concept of null infinity). To overcome this, Penrose launched his cosmic censorship conjecture(s), whose evolution we discuss. In particu…
We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by higher dimensional Tolman-Bondi space-times. The naked singularities are found to be gravitationally strong in the sense of Tipler. Higher dimensions seem to favour black holes rather than naked singularities.
A brief review is given of three recent results concerning classical solutions of gravitational theories: (1) With asymptotically anti de Sitter boundary conditions, there are matter theories satisfying the positive energy theorem which violate cosmic censorship. (2) Despite supersymmetry, there are solutions to N=8 supergravity in which the total gravitational energy is arbitrarily negative. This theory can also violate cosmic censorship. (3) A large class of supersymmetric compactifications (including all simply connected Calabi-Yau manifolds) have solutions with negative four dimensional ef…
We show that the naked singularities arising in dust collapse from smooth initial data (which include those discovered by Eardley and Smarr, Christodoulou, and Newman) are removed when we make transition to higher dimensional spacetimes. The cosmic censorship is then restored for dust collapse which will always produce a black hole as the collapse end state for dimensions $D\ge6$, under conditions to be motivated physically such as the smoothness of initial data from which the collapse develops.
We discuss several aspects of cosmic censorship hypothesis. There is evidence both in favor and against the hypothesis. On one hand one can prove that cosmic censorship holds in several special cases and on the other hand there is a number of special solutions of Einstein equations in which it is violated. One way to resolve cosmic censorship problem is to test it observationally. We point out to several possibilities of such tests using present and future instruments.
Present knowledge about the nature of spacetime singularities in the context of classical general relativity is surveyed. The status of the BKL picture of cosmological singularities and its relevance to the cosmic censorship hypothesis are discussed. It is shown how insights on cosmic censorship also arise in connection with the idea of weak null singularities inside black holes. Other topics covered include matter singularities and critical collapse. Remarks are made on possible future directions in research on spacetime singularities.
We consider (four dimensional) gravity coupled to a scalar field with potential V(ϕ). The potential satisfies the positive energy theorem for solutions that asymptotically tend to a negative local minimum. We show that for a large class of such potentials, there is an open set of smooth initial data that evolve to naked singularities. Hence cosmic censorship does not hold for certain reasonable matter theories in asymptotically anti de Sitter spacetimes. The asymptotically flat case is more subtle. We suspect that potentials with a local Minkowski minimum may similarly lead to violations of co…
We investigate the instability of the Cauchy horizon caused by causality violation in the compact vacuum universe with the topology $B\times {\bf S}^{1}\times {\bf R}$, which Moncrief and Isenberg considered. We show that if the occurrence of curvature singularities are restricted to the boundary of causality violating region, the whole segments of the boundary become curvature singularities. This implies that the strong cosmic censorship holds in the spatially compact vacuum space-time in the case of the causality violation. This also suggests that causality violation cannot occur for a compa…
The hypothesis of cosmic censorship (CCH) plays a crucial role in classical general relativity, namely to ensure that naked singularities would never emerge, since it predicts that whenever a singularity is formed an event horizon would always develop around it as well, to prevent the former from interacting directly with the rest of the Universe. Should this not be so, naked singularities could eventually form, in which case phenomena beyond our understanding and ability to predict could occur, since at the vicinity of the singularity both predictability and determinism break down even at the…
This article gives an elementary review of gravitational collapse and the cosmic censorship hypothesis. Known models of collapse resulting in the formation of black holes and naked singularities are summarized. These models, when taken together, suggest that the censorship hypothesis may not hold in classical general relativity. The nature of the quantum processes that take place near a naked singularity, and their possible implication for observations, is briefly discussed.
A thought experiment considered recently in the literature, in which it is investigated whether a dyonic Kerr-Newman black hole can be destroyed by overcharging or overspinning it past extremality by a massive complex scalar test field, is revisited. Another derivation of the result that this is not possible, i.e. the weak cosmic censorship is not violated in this thought experiment, is given. The derivation is based on conservation laws, on a null energy condition, and on specific properties of the metric and the electromagnetic field of dyonic Kerr-Newman black holes. The metric is kept fixe…
Cosmic censorship is known to fail in some well-controlled phenomena, calling into question the predictive power of General Relativity and opening up the possibility of observing Planck-scale physics. We propose that the cosmic censorship conjecture can be amended so that its spirit prevails. Naked singularities that, classically, have zero mass are allowed. Physically, these are Planck-sized `black holes', which evaporate in a few Planck times. General Relativity fails only for a tiny interval in time, to then quickly regain control in a Miltonian evolution that returns us to the predictive p…
We analyze the Hawking evaporation process of Reissner-Nordström black holes. It is shown that the characteristic radiation quanta emitted by the charged black holes may turn near-extremal black-hole spacetimes into horizonless naked singularities. The present analysis therefore reveals the intriguing possibility that the semi-classical Hawking evaporation process of black holes may violate the fundamental Penrose cosmic censorship conjecture.
We study vacuum domain walls in a class of four-dimensional $N=1$ supergravity theories where along with the matter field, forming the wall, there is more than one ``dilaton'', each respecting $SU(1,1)$ symmetry in their sub-sector. We find {\it supersymmetric} (planar, static) walls, interpolaing between Minkowski vacuum and a new class of supersymmetric vacua which have a naked (planar) singularity. Such walls provide the first example of supersymmetric classical ``solitons'' with naked singularities, and thus violate the (strong) cosmic censorship conjecture within a supersymmetric theory.
Gravitational collapse of radiation shells in a non self-similar higher dimensional spherically symmetric spacetime is studied. Strong curvature naked singularities form for a highly inhomogeneous collapse, violating the cosmic censorship conjecture. As a special case, self similar models can be constructed.
Motivated by the recent researches of black holes with NUT charge, we investigate the validity of the weak cosmic censorship conjecture for Kerr-Taub-NUT black hole with a test massive scalar field and a test particle, respectively. For the scalar field scattering gedanken experiment, we consider an infinitesimal time interval process. The result shows that both extremal and near-extremal Kerr-Taub-NUT black holes cannot be over-spun. For the test particle thought experiment, the study suggests that extremal Kerr-Taub-NUT black hole cannot be over-spun; while near-extremal Kerr-Taub-NUT black …
This article gives an elementary overview of the end-state of gravitational collapse according to classical general relativity. The focus of discussion is the formation of black holes and naked singularities in various physically reasonable models of gravitational collapse. Possible implications for the cosmic censorship hypothesis are outlined.
The cosmic censorship conjecture essentially states that naked singularities should not form from generic initial conditions. Since black hole parameters can change their values under Hawking evaporation, one has to ask whether it is possible to reach extremality by simply waiting for the black hole to evaporate. If so a slight perturbation would likely render the singularity naked. Fortunately, at least for the case of asymptotically flat 4-dimensional Reissner-Nordström black hole, Hiscock and Weems showed that it can never reach extremality despite the fact that for a sufficiently massive b…
We study the time delay between successive relativistic images in gravitational lensing as a possible discriminator between various collapse end states and hence as a probe of cosmic censorship. Specifically we consider both black hole and naked singularity spacetimes admitting photon spheres where an infinite number of relativistic Einstein Rings can be formed at almost the same radius and naked singularity spacetimes without a photon sphere where multiple relativistic Einstein Rings can form almost up to the center of the lens. The metrics we have considered to sample these scenarios are the…
Exact nonstatic spherically symmetric black-hole solution of the higher dimensional Einstein-Yang-Mills equations for a null dust with Yang-Mills gauge charge are obtained by employing Wu-Yang \textit{ansatz}, namely, HD-EYM Vaidya solution. It is interesting to note that gravitational contribution of YM gauge charge for this ansatz is indeed opposite (attractive rather than repulsive) that of Maxwell charge. It turns out that the gravitational collapse of null dust with YM gauge charge admit strong curvature shell focusing naked singularities violating cosmic censorship. However, there is sig…
Israel's proof of the third law of black hole dynamics is based on the semi-rigidity assumption which requires that the areas of the outermost trapped surfaces are preserved. We argue that the condition that the area of the event horizon should not decrease is necessary -but not sufficient- for the semi-rigidity assumption to hold. It is known that the presence of a naked singularity in the exterior region invalidates Hawking's proof of the area theorem. In this sense, the third law assumes the validity of the strong form of the cosmic censorship conjecture, contrary to general acceptance. Sti…
The present analytical understanding on the nature of the singularities which form at the endstate of gravitational collapse of massive fluid bodies ("stars") is reviewed. Special emphasis is devoted to the issue of physical reasonability of the models.
We perform extensive nonlinear numerical simulations of the spherical collapse of (charged) wavepackets onto a charged black hole within Einstein-Maxwell theory and in Einstein-Maxwell-scalar theory featuring nonminimal couplings and a spontaneous scalarization mechanism. We confirm that black holes in full-fledged Einstein-Maxwell theory cannot be overcharged past extremality and no naked singularities form, in agreement with the cosmic censorship conjecture. We show that naked singularities do not form even in Einstein-Maxwell-scalar theory, although it is possible to form scalarized black h…
The hypothesis of cosmic censorship plays a crucial role in classical general relativity, namely, to ensure that naked singularities would never occur from the black hole singularity. In this paper, we will present how energy conditions prohibit forming the naked singularity in the spherical perfect fluid collapse, and thus the strong cosmic censorship conjecture hold in this model. We also show that this result can be extended to the cosmological constant background.
For almost half of the one hundred year history of Einstein's theory of general relativity, Strong Cosmic Censorship has been one of its most intriguing conjectures. The SCC conjecture addresses the issue of the nature of the singularities found in most solutions of Einstein's gravitational field equations: Are such singularities generically characterized by unbounded curvature? Is the existence of a Cauchy horizon (and the accompanying extensions into spacetime regions in which determinism fails) an unstable feature of solutions of Einstein's equations? In this short review article, after bri…
Challenging the Weak Cosmic Censorship with Phantom Fields
Sapienza Università di Roma（罗马第一大学）；INFN, Sezione di Roma（罗马国家核物理研究所）；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））
We examine the achronal averaged null energy condition~(ANEC) for a class of conformal field theories~(CFT) at strong coupling in curved spacetime. By applying the AdS/CFT duality, we find holographic models which violate the achronal ANEC for $3+1$ and $4+1$-dimensional boundary theories. In our model, the bulk spacetime is an asymptotically AdS vacuum bubble solution with neither causality violation nor singularities. The conformal boundary of our bubble solution is asymptotically flat and is causally proper in the sense that a "fastest null geodesics" connecting any two points on the bounda…
We analyze the properties of a Kerr-like wormhole supported by phantom matter, which is an exact solution of the Einstein-phantom field equations. It is shown that the solution has a naked ring singularity which is unreachable to null geodesics falling freely from the outside. Similarly to Roger Penrose's cosmic censorship, that states that all naked singularities in the Universe must be protected by event horizons, here we conjecture from our results that a naked singularity can also be fully protected by the intrinsic properties of a wormhole's throat.
It has been suggested by Israel that the Kerr singularity cannot be strong in the sense of Tipler, for it tends to cause repulsive effects. We show here that, contrary to that suggestion, nearly all null geodesics reaching this singularity do in fact terminate in Tipler's strong curvature singularity. Implications of this result are discussed in the context of an earlier cosmic censorship theorem which constraints the occurrence of Kerr-like naked singularities in generic collapse situations.
There is a claim that a static charged black hole (Reissner-Nordström black hole) can be overcharged by absorbing a charged test particle. If it is true, it might give a counter example to the weak cosmic censorship conjecture, which states that spacetime singularities are never observed by a distant observer. However, so far the proposed process has only been analyzed within a test particle approximation. Here we claim that the back reaction effects of a charged particle cannot be neglected when judging whether the suggested process is really a counter example to the cosmic censorship conject…
In general relativity, gravitational collapse of matter fields ends with the formation of a spacetime singularity, where the matter density becomes infinite and standard physics breaks down. According to the weak cosmic censorship conjecture, singularities produced in the gravitational collapse cannot be seen by distant observers and must be hidden within black holes. The validity of this conjecture is still controversial and at present we cannot exclude that naked singularities can be created in our Universe from regular initial data. In this paper, we study the radiation emitted by a collaps…
End state of gravitational collapse and the related cosmic censorship conjecture continue to be amongst the most important open problems in gravitation physics today. My purpose here is to bring out several aspects related to gravitational collapse and censorship, which may help towards a better understanding of the issues involved. Possible physical constraints on gravitational collapse scenarios are considered. It is concluded that the best hope for censorship lies in analyzing the genericity and stability properties of the currently known classes of collapse models which lead to the formati…
We review the properties of naked time-like singularities in the General Relativity and quantum effects in their vicinity. We demonstrate that only line-like singularities can be formed by a collapse and are the only candidates to break the Cosmic Censorship Principle.
Choptuik has demonstrated that naked singularities can arise in gravitational collapse from smooth, asymptotically flat initial data, and that such data have codimension one in spherical symmetry. Here we show, for perfect fluid matter with equation of state $p=ρ/3$, by perturbing around spherical symmetry, that such data have in fact codimension one in the full phase space, at least in a neighborhood of spherically symmetric data.
Gravitational collapse of radiation in an anti-de Sitter background is studied. For the spherical case, the collapse proceeds in much the same way as in the Minkowski background, i.e., massless naked singularities may form for a highly inhomogeneous collapse, violating the cosmic censorship, but not the hoop conjecture. The toroidal, cylindrical and planar collapses can be treated together. In these cases no naked singularity ever forms, in accordance with the cosmic censorship. However, since the collapse proceeds to form toroidal, cylindrical or planar black holes, the hoop conjecture in an …
