The repulsive nature of naked singularities from the point of view of Quantum Mechanics

We use the Dirac equation coupled to a background metric to examine what happens to quantum-mechanical observables like the probability density and the radial current in the vicinity of a naked singularity of the Reissner–Nordström type. We find that the wave function of the Dirac particle is regular in the point of the singularity. We show that the probability density is exactly zero at the singularity reflecting quantum-mechanically the repulsive nature of the naked singularity. Furthermore, the surface integral of the radial current over a sphere in the vicinity of the naked singularity turns out to be also zero.     

Gravitational Collapse in Higher Dimensional Space-Time

Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space-time and the appearance of a naked singularity has been analyzed both for the non-marginal and the marginally bound cases. It has been shown that a naked singularity is possible for any arbitrary dimension in the non-marginally bound case. For the marginally bound case we have examined the radial null geodesics from the singularity and found that a naked singularity is possible up to five dimensions.     

Distinguishing between Kerr and rotating JNW space-times via frame dragging and tidal effects

We investigate two physical quantities that might observationally distinguish between Kerr black holes and rotating naked singularities. These are the Lense–Thirring precession frequency as measured by a Copernican observer, and tidal forces. We establish strong enhancement for both these quantities due to a Janis–Newman–Winicour naked singularity background, as compared to the Kerr case. We first show that the precession frequency of a test gyroscope at a given radius can be enhanced by almost an order of magnitude in the background of the naked singularity, as compared to the Kerr black hole. We then show that a critical mass for celestial objects below which these disintegrate due to tidal forces might increase by more than an order of magnitude in the naked singularity background, compared to the black hole. Our results complement the existing ones in the literature regarding differences in observable quantities in such backgrounds, and might be of significance in futuristic experiments.     

Classical and quantum properties of a two-sphere singularity

Recently Böhmer and Lobo have shown that a metric due to Florides, which has been used as an interior Schwarzschild solution, can be extended to reveal a classical singularity that has the form of a two-sphere. Here the singularity is shown to be a naked scalar curvature singularity that is both timelike and gravitationally weak. It is also shown to be a quantum singularity because the Klein–Gordon operator associated with quantum mechanical particles approaching the singularity is not essentially self-adjoint.     

On the Global Visibility of the Singularity in Quasi-Spherical Collapse

We analyze here the issue of local versus global visibility of a singularity that forms in gravitational collapse of a dust cloud, which has important implications for the weak and strong versions of the cosmic censorship hypothesis. We find conditions for when a singularity will be only locally naked, rather than being globally visible, thus preserving the weak censorship hypothesis. The conditions for the formation of a black hole or a naked singularity in the Szekeres quasi-spherical collapse models are worked out. The causal behaviour of the singularity curve is studied by examining the outgoing radial null geodesics, and the final outcome of collapse is related to the nature of the regular initial data specified on an initial hypersurface from which the collapse evolves. An interesting feature that emerges is that the singularity in Szekeres spacetimes can be directionally naked.     

Dilatonic effects near naked singularities

Static spherically symmetric solutions of 4d Brans–Dicke theory include a set of naked singularity solutions. Dilatonic effects near the naked singularities result in either a shielding or an antishielding effect from intruding massive test particles. One result is that for a portion of the solution parameter space, no communication between the singularity and a distant observer is possible via massive particle exchanges. Kaluza–Klein gravity is considered as a special case.     

Gravitational collapse and naked singularities

Gravitational collapse is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for research in this field. In the absence of a general proof for censorship, many examples have been proposed, in which naked singularity is the outcome of gravitational collapse. Recent developments have revealed that there are examples of naked singularity formation in the collapse of physically reasonable matter fields, although the stability of these examples is still uncertain. We propose the concept of ‘effective naked singularities’, which will be quite helpful because general relativity has limitation in its application at the high-energy end. The appearance of naked singularities is not detestable but can open a window for the new physics of strongly curved space-times.     

Naked Singularity of the Vaidya-de Sitter Spacetime and Cosmic Censorship Conjecture

We investigate the formation of a locally nakedsingularity in the collapse of radiation shells in anexpanding Vaidya-de Sitter background. This is achievedby considering the behaviour of non-spacelikeand radial geodesics originating at thesingularity. A specific condition is determined for theexistence of radially outgoing, null geodesicsoriginating at the singularity which, when thiscondition is satisfied, becomes locally naked. Thiscondition turns out to be the same as that in thecollapse of radiation shells in an asymptotically flatbackground. Therefore we have established, at least forthe case considered here, that the asymptoticflatness of the spacetime is not essential for thedevelopment of a locally naked singularity. Our resultthen unequivocally supports the view that no specialrole be given to asymptotic observers (or, for thatmatter, any set of observers) in the formulation of theCosmic Censorship Hypothesis.     

Evaporating black hole in Vaidya metric

The energy momentum tensor for an evaporating black hole modelled with Vaidya metric is computed. The result indicates that the evaporation does not create a naked singularity.     

Spherically symmetric inhomogeneous dust collapse in higher dimensional space-time and cosmic censorship hypothesis

We consider a collapsing spherically symmetric inhomogeneous dust cloud in higher dimensional space-time. We show that the central singularity of collapse can be a strong curvature or a weak curvature naked singularity depending on the initial density distribution.     

Gamma-Ray Bursts and Quantum Cosmic Censorship

Gamma-ray bursts are believed to result from the coalescence of binary neutron stars. However, the standard proposals for conversion of the gravitational energy to thermal energy have difficulties. We show that if the merger of the two neutron stars results in a naked singularity, instead of a black hole, the ensuing quantum particle creation can provide the requisite thermal energy in a straightforward way. The back-reaction of the created particles can avoid the formation of the naked singularity predicted by the classical theory. Hence cosmic censorship holds in the quantum theory, even if it were to be violated in classical general relativity.     

Horizonless,singularity-free,compact shells satisfying NEC

Gravitational collapse singularities are undesirable, yet inevitable to a large extent in General Relativity. When matter satisfying null energy condition (NEC) collapses to the extent a closed trapped surface is formed, a singularity is inevitable according to Penrose’s singularity theorem. Since positive mass vacuum solutions are generally black holes with trapped surfaces inside the event horizon, matter cannot collapse to an arbitrarily small size without generating a singularity. However, in modified theories of gravity where positive mass vacuum solutions are naked singularities with no trapped surfaces, it is reasonable to expect that matter can collapse to an arbitrarily small size without generating a singularity. Here we examine this possibility in the context of a modified theory of gravity with torsion in an extra dimension. We study singularity-free static shell solutions to evaluate the validity of NEC on the shell. We find that with sufficiently high pressure, matter can be collapsed to arbitrarily small size without violating NEC and without producing a singularity.     

Globally noncausal space-times. II. Naked singularities and curvature conditions

In this paper we prove that if there is a naked singularity, then there will be some null geodesic, reaching ⁺ from the singularity, which does not satisfy the strong curvature condition regardless of whether causality is violated or not. Assuming that a naked singularity is a strong curvature singularity only sufficiently far to the future, we prove that strong causality is violated arbitrarily close to ⁺.Work partially supported by the Nuffield Foundation and by the Consiglio Nazionale delle Ricerche of Italy under contract N.CT 81.00532.02.     

Quantum evaporation of a naked singularity

We investigate here quantum effects in gravitational collapse of a scalar field model which classically leads to a naked singularity. We show that nonperturbative semiclassical modifications near the singularity, based on loop quantum gravity, give rise to a strong outward flux of energy. This leads to the dissolution of the collapsing cloud before the singularity can form. Quantum gravitational effects thus censor naked singularities by avoiding their formation. Further, quantum gravity induced mass flux has a distinct feature which may lead to a novel observable signature in astrophysical bursts.     

Does string theory solve the puzzles of black hole evaporation?

We point out that the massive modes of closed superstring theories may play a crucial role in the last stages of black hole evaporation. If the Bekenstein-Hawking entropy describes the true degeneracy of a black hole — implying loss of quantum coherence and the unitary evolution of quantum states-it becomes entropically favorable for an evaporating black hole to make a transition to a state of massive string modes. This in turn may decay into massless modes of the string (radiation) avoiding the naked singularity exposed by black hole evaporation in the semiclassical picture. Alternatively, quantum coherence may be maintained if the entropy of an evaporating black hole is much larger than that given by the Bekenstein-Hawking formula. In that case, however, the transition to massive string modes is unlikely. String theories might thus resolve the difficulty of the naked singularity, but it appears likely that they will still involve loss of quantum coherence.This essay received the first award from the Gravity Research Foundation for the year 1986 — Ed.     

Spherical Gravitational Collapse: Tangential Pressure and Related Equations of State

We derive an equation for the acceleration of a fluid element in the spherical gravitational collapse of a bounded compact object made up of an imperfect fluid. We show that non-singular as well as singular solutions arise in the collapse of a fluid initially at rest and having only a tangential pressure. We obtain an exact solution of the Einstein equations, in the form of an infinite series, for collapse under tangential pressure with a linear equation of state. We show that if a singularity forms in the tangential pressure model, the conditions for the singularity to be naked are exactly the same as in the model of dust collapse.     

Fermionic greybody factors of two and five-dimensional dilatonic black holes

We analyze the persistence of curvature singularities when analyzed using quantum theory. First, quantum test particles obeying the Klein–Gordon and Chandrasekhar–Dirac equation are used to probe the classical timelike naked singularity. We show that the classical singularity is felt even by our quantum probes. Next, we use loop quantization to resolve a singularity hidden beneath the horizon. The singularity is resolved in this case.     

Instability of black hole formation under small pressure perturbations

We investigate here the spectrum of gravitational collapse endstates when arbitrarily small perfect fluid pressures are introduced in the classic black hole formation scenario as described by Oppenheimer, Snyder and Datt (OSD) (Oppenheimer and Snyder in Phys Rev 56:455, 1939; Datt in Zs f Phys 108:314, 1938). This extends a previous result on tangential pressures (Joshi and Malafarina Phys Rev D 83:024009, 2011) to the physically more realistic scenario of perfect fluid collapse. The existence of classes of pressure perturbations is shown explicitly, which has the property that injecting any smallest pressure changes the final fate of the dynamical collapse from a black hole to a naked singularity. It is therefore seen that any smallest neighborhood of the OSD model, in the space of initial data, contains collapse evolutions that go to a naked singularity outcome. This gives an intriguing insight on the nature of naked singularity formation in gravitational collapse.     

Stability of naked singularity arising in gravitational collapse of Type I matter fields

Considering gravitational collapse of Type I matter fields, we prove that, given an arbitrary C²-mass functionM(r, v) and a C¹-functionh(r, v) (through the corresponding C¹-metric functionν(t, r)), there exist infinitely many choices of energy distribution functionb(r) such that the ’true’ initial data(M, h(r,v)) leads the collapse to the formation of naked singularity. We further prove that the occurrence of such a naked singularity is stable with respect to small changes in the initial data. We remark that though the initial data leading to both black hole (BH) and naked singularity (NS) form a ’big’ subset of the true initial data set, their occurrence is not generic. The terms ’stability’ and ’genericity’ are appropriately defined following the theory of dynamical systems. The particular case of radial pressurep _r (r) has been illustrated in details to get a clear picture of how naked singularity is formed and how, it is stable with respect to initial data.