Acausality in Gowdy spacetimes

We present a parametrization of T ³ and S ¹ × S ² Gowdy cosmological models which allows us to study both types of topologies simultaneously. We show that there exists a coordinate system in which the general solution of the linear polarized special case (with both topologies) has exactly the same functional dependence. This unified parametrization is used to investigate the existence of Cauchy horizons at the cosmological singularities, leading to a violation of the strong cosmic censorship conjecture. Our results indicate that the only acausal spacetimes are described by the Kantowski-Sachs and the Kerr-Gowdy metrics.     

Essay: Cosmic Censorship: The Role of Quantum Gravity

The cosmic censorship hypothesis introduced by Penrose thirty years ago is still one of the most important open questions in classical general relativity. In this essay we put forward the idea that cosmic censorhip is intrinsically a quantum gravity phenomena. To that end, we construct a gedanken experiment in which cosmic censorship is violated within the purely classical framework of general relativity. We prove, however, that quantum effects restore the validity of the conjecture. This suggests that classical general relativity is inconsistent and that cosmic censorship might be enforced only by a quantum theory of gravity.     

Thermodynamics and weak cosmic censorship conjecture of an AdS black hole with a monopole in the extended phase space

The first law of black hole thermodynamics has been shown to be valid in the extended phase space.However,the second law and the weak cosmic censorship conjecture have not been investigated extensively.We investigate the laws of thermodynamics and the weak cosmic censorship conjecture of an AdS black hole with a global monopole in the extended phase space in the case of charged particle absorption.It is shown that the first law of thermodynamics is valid,while the second law is violated for the extremal and near-extremal black holes.Moreover,we find that the weak cosmic censorship conjecture is valid only for the extremal black hole,and that it can be violated for the near-extremal black holes,which is different from the previous results.     

Demise of the Cosmic Censor?

Initial data for general relativity may be such that there are trapped surfaces on a spatial initial data surface. Penrose has proposed that if the cosmic censorship hypothesis is true, the ADM mass M of asymptotically flat initial data and the area A of the outermost apparent horizon surface should satisfy the inequality A 16M². Initial data which does not satisfy this inequality may be viewed as providing a counterexample of the cosmic censorship conjecture. We describe initial data that appears to violate this inequality.     

Cosmic censorship,black holes,and particle orbits

Perhaps one of the main reasons for believing in the cosmic censorship hypothesis is the disquieting nature of the alternative: the existence of naked singularities, and hence loss of predictability, the possibility of closed timelike lines, and so forth. The consequences of assuming the cosmic censorship hypothesis can also be somewhat strange and unexpected. In particular, we apply Hawking's black hole area theorem to the study of particle orbits near a Schwarzschild black hole. If the cosmic censorship hypothesis (and hence the area theorem) is true, then there exist stable near-circular orbits arbitrarily close to the horizon atr=2M.This essay was awarded the third prize for 1978 by the Gravity Research Foundation. (Ed.)Work supported in part by the National Science Foundation contract PHY76-20029.     

Weak cosmic censorship conjecture and thermodynamics in quintessence AdS black hole under charged particle absorption

Considering the cosmological constant as the pressure, this study addresses the laws of thermodynamics and weak cosmic censorship conjecture in the Reissner-Nordstr?m-AdS black hole surrounded by quintessence dark energy under charged particle absorption. The first law of thermodynamics is found to be valid as a particle is absorbed by the black hole. The second law, however, is violated for the extremal and near-extremal black holes, because the entropy of these black hole decrease. Moreover, we find that the extremal black hole does not change its configuration in the extended phase space, implying that the weak cosmic censorship conjecture is valid. Remarkably, the near-extremal black hole can be overcharged beyond the extremal condition under charged particle absorption. Hence, the cosmic censorship conjecture could be violated for the near-extremal black hole in the extended phase space. For comparison, we also discuss the first law, second law, and the weak cosmic censorship conjecture in normal phase space, and find that all of them are valid in this case.     

Weak cosmic censorship conjecture in BTZ black holes with scalar fields

The weak cosmic censorship conjecture in the near-extremal BTZ black hole has been tested using test particles and fields.It has been claimed that such a black hole can be overspun.In this paper,we review the thermodynamics and weak cosmic censorship conjecture in BTZ black holes using the scattering of a scalar field.The first law of thermodynamics in the non-extremal BTZ black hole is recovered.For the extremal and near-extremal black holes,due to the divergence of the variation of entropy,we test the weak cosmic censorship conjecture by evaluating the minimum of the function f,and find that both the extremal and near-extremal black holes cannot be overspun.     

Weak cosmic censorship: as strong as ever

Spacetime singularities that arise in gravitational collapse are always hidden inside of black holes. This is the essence of the weak cosmic censorship conjecture. The hypothesis, put forward by Penrose 40 years ago, is still one of the most important open questions in general relativity. In this Letter, we reanalyze extreme situations which have been considered as counterexamples to the weak cosmic censorship conjecture. In particular, we consider the absorption of scalar particles with large angular momentum by a black hole. Ignoring back reaction effects may lead one to conclude that the incident wave may overspin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when back reaction effects are properly taken into account, the stability of the black-hole event horizon is irrefutable. We therefore conclude that cosmic censorship is actually respected in this type of gedanken experiments.     

Classical and quantum models of strong cosmic censorship

The cosmic censorship conjecture states that naked singularities should not evolve from regular initial conditions in general relativity. In its strong form the conjecture asserts that space-times with Cauchy horizons must always be unstable and thus that thegeneric solution of Einstein's equations must be inextendible beyond its maximal Cauchy development. In this paper we shall show that one can construct an infinite-dimensional family ofextendible cosmological solutions similar to Taub-NUT space-time. However, we shall also show that each of these solutions is unstable in precisely the way demanded by strong cosmic censorship. Finally we show that quantum fluctuations in the metric always provide (though in an unexpectedly subtle way) the “generic perturbations” which destroy the Cauchy horizons in these models.     

Does a cosmic censor exist?

A distinction is drawn between the event horizon conjecture (EHC), the conjecture that an event horizon forms in a gravitational collapse, and cosmic censorship, the idea that every singularity which develops in the course of collapse must be enclosed within a horizon. It is argued that a body of circumstantial evidence seems to favor EHC, but cosmic censorship seems contraindicated.Work partially supported by the Natural Sciences and Engineering Research Council of Canada.     

Naked singularity formation in $${f({\mathcal R})}$$ gravity

We study the gravitational collapse of a star with barotropic equation of state p = wρ in the context of f(R){f({\mathcal R})} theories of gravity. Utilizing the metric formalism, we rewrite the field equations as those of Brans-Dicke theory with vanishing coupling parameter. By choosing the functionality of Ricci scalar as f(R)=aR^m{f({\mathcal R})=\alpha{\mathcal R}^{m}} , we show that for an appropriate initial value of the energy density, if α and m satisfy certain conditions, the resulting singularity would be naked, violating the cosmic censorship conjecture. These conditions are the ratio of the mass function to the area radius of the collapsing ball, negativity of the effective pressure, and the time behavior of the Kretschmann scalar. Also, as long as parameter α obeys certain conditions, the satisfaction of the weak energy condition is guaranteed by the collapsing configuration.     

Return of the quantum cosmic censor

The influential theorems of Hawking and Penrose demonstrate that spacetime singularities are ubiquitous features of general relativity, Einstein's theory of gravity. The utility of classical general relativity in describing gravitational phenomena is maintained by the cosmic censorship principle. This conjecture, whose validity is still one of the most important open questions in general relativity, asserts that the undesirable spacetime singularities are always hidden inside of black holes. In this Letter we reanalyze extreme situations which have been considered as counterexamples to the cosmic censorship hypothesis. In particular, we consider the absorption of fermion particles by a spinning black hole. Ignoring quantum effects may lead one to conclude that an incident fermion wave may over spin the black hole, thereby exposing its inner singularity to distant observers. However, we show that when quantum effects are properly taken into account, the integrity of the black-hole event horizon is irrefutable. This observation suggests that the cosmic censorship principle is intrinsically a quantum phenomena.     

Thermodynamics and weak cosmic censorship conjecture of BTZ black holes in extended phase space

As a charged fermion drops into a BTZ black hole, the laws of thermodynamics and the weak cosmic censorship conjecture are investigated in both the normal and extended phase space, where the cosmological parameter and renormalization length are regarded as extensive quantities. In the normal phase space, the first and second law of thermodynamics, and the weak cosmic censorship are found to be valid. In the extended phase space, although the first law and weak cosmic censorship conjecture remain valid, the second law is dependent on the variation of the renormalization energy d K. Moreover, in the extended phase space, the configurations of extremal and near-extremal black holes are not changed, as they are stable, while in the normal phase space, the extremal and near-extremal black holes evolve into non-extremal black holes.     

Neighborhoods of Cauchy horizons in cosmological spacetimes with one killing field

In this paper we show how to construct an infinite dimensional family of analytic, vacuum spacetimes which each have (i) T³ × R topology, (ii) a smooth, compact Cauchy horizon, and (iii) a single Killing vector field which is spacelike in the globally hyperbolic region, null on the horizon and timelike in the (acausal) extension. The key idea is to use the horizons themselves as initial data surfaces and to prove the local existence of solutions using a version of the Cauchy-Kowalewski theorem. Factoring by the action of analytic, horizon preserving diffeomorphisms we define a “space of extendible vacuum spacetimes” of the given symmetry type and show (modulo certain smoothness estimates which we do not attempt to derive) that this space defines a Lagrangian submanifold of the usual phase space for Einstein's equations. We also study the linear perturbations of a class of the extendible spacetimes and show that the generic such perturbation blows up near the background solution's Cauchy horizon. This result, though limited by the linearity of the approximation, conforms to the usual picture of unstable Cauchy horizons demanded by the strong cosmic censorship conjecture.     

Global properties of Gowdy spacetimes with T3 × R topology

We study the global properties of the Gowdy metrics generated by Cauchy data on the 3-torus. We show that the boundaries of the maximal Cauchy developments of Gowdy initial data sets are always “crushing singularities” in the sense of Eardley and Smarr. This means that each solution admits a slicing in which tr K(t) (the trace of the second fundamental form induced on the surface Σ_t of the slicing) uniformly blows up as t approaches its limiting value. A theorem of Hawking shows that the maximal Cauchy development cannot extend beyond the boundary at which tr K blows up and our result shows that no singularities arise to halt the evolution until this boundary is reached. Thus each maximal Cauchy development is always as large as it can be, consistent with Hawking's theorem. We discuss the relevance of this result to the strong cosmic censorship conjecture and the question of when the crushing singularities are in fact curvature singularities.     

Strong cosmic censorship for a scalar field in an Einstein-Maxwell-Gauss-Bonnet-de Sitter black hole

It has been shown that the Christodoulou version of the strong cosmic censorship(SCC)conjecture can be violated for a scalar field in a near-extremal Reissner-Nordstrom-de Sitter black hole.In this paper,we investigate the effects of higher derivative corrections to the Einstein-Hilbert action on the validity of SCC,by considering a neutral massless scalar perturbation in 5 -and 6 -dimensional Einstein-Maxwell-Gauss-Bonnet-de Sitter black holes.Our numerical results show that the higher derivative term plays a different role in the d=5 case than it does in the d=6 case.For d=5 ,the SCC violation region increases as the strength of the higher derivative term increases.For d=6 ,the SCC violation region first increases and then decreases as the higher derivative correction becomes stronger,and SCC can always be restored for a black hole with a fixed charge ratio when the higher derivative correction is strong enough.Finally,we find that the C² version of SCC is respected in the d=6 case,but can be violated in some near-extremal regimes in the d=5 case.     

The Einstein Constant c in Light of Mach's Principle. Cosmological Applications

In a recent paper, O. Costa de Beauregard shows that Mach's conjecture can be expressed by the equation U=c ² (U denoting the cosmological potential). This result leads us to a geometrical interpretation of Einstein's constant c (the so-called velocity of light) which appears as intimately connected to the expansion of the universe. We also present some cosmological consequences of that interpretation for the horizon problem, for the problem of the homogeneity of the cosmic background radiation, and for the problem of the flatness of the universe.     

Dyonic Kerr–Newman black holes,complex scalar field and cosmic censorship

We construct a gedanken experiment, in which a weak wave packet of the complex massive scalar field interacts with a four-parameter (mass, angular momentum, electric and magnetic charges) Kerr–Newman black hole. We show that this interaction cannot convert an extreme the black hole into a naked sigularity for any black hole parameters and any generic wave packet configuration. The analysis therefore provides support for the weak cosmic censorship conjecture.     

A Proof of the Geroch–Horowitz–Penrose Formulation of the Strong Cosmic Censor Conjecture Motivated by Computability Theory

In this paper we present a proof of a mathematical version of the strong cosmic censor conjecture attributed to Geroch–Horowitz and Penrose but formulated explicitly by Wald. The proof is based on the existence of future-inextendible causal curves in causal pasts of events on the future Cauchy horizon in a non-globally hyperbolic space-time. By examining explicit non-globally hyperbolic space-times we find that in case of several physically relevant solutions these future-inextendible curves have in fact infinite length. This way we recognize a close relationship between asymptotically flat or anti-de Sitter, physically relevant extendible space-times and the so-called Malament–Hogarth space-times which play a central role in recent investigations in the theory of “gravitational computers”. This motivates us to exhibit a more sharp, more geometric formulation of the strong cosmic censor conjecture, namely “all physically relevant, asymptotically flat or anti-de Sitter but non-globally hyperbolic space-times are Malament–Hogarth ones”. Our observations may indicate a natural but hidden connection between the strong cosmic censorship scenario and the Church–Turing thesis revealing an unexpected conceptual depth beneath both conjectures.     

Symmetries of cosmological Cauchy horizons

We consider analytic vacuum and electrovacuum spacetimes which contain a compact null hypersurface ruled byclosed null generators. We prove that each such spacetime has a non-trivial Killing symmetry. We distinguish two classes of null surfaces, degenerate and non-degenerate ones, characterized by the zero or non-zero value of a constant analogous to the “surface gravity” of stationary black holes. We show that the non-degenerate null surfaces are always Cauchy horizons across which the Killing fields change from spacelike (in the globally hyperbolic regions) to timelike (in the acausal, analytic extensions). For the special case of a null surface diffeomorphic toT ³ we characterize the degenerate vacuum solutions completely. These consist of an infinite dimensional family of “plane wave” spacetimes which are entirely foliated by compact null surfaces. Previous work by one of us has shown that, when one dimensional Killing symmetries are allowed, then infinite dimensional families of non-degenerate, vacuum solutions exist. We recall these results for the case of Cauchy horizons diffeomorphic toT ³ and prove the generality of the previously constructed non-degenerate solutions. We briefly discuss the possibility of removing the assumptions of closed generators and analyticity and proving an appropriate generalization of our main results. Such a generalization would provide strong support for the cosmic censorship conjecture by showing that causality violating, cosmological solutions of Einstein's equations are essentially an artefact of symmetry.