The structure of naked singularity in self-similar gravitational collapse

We study the structure and formation of naked singularities in selfsimilar gravitational collapse for an adiabatic perfect fluid. Conditions are obtained for the singularity to be either locally or globally naked and for the families of non-spacelike geodesics to terminate at the singularity in past. This is shown to be a strong curvature naked singularity in a powerful sense and an interesting relationship is pointed out between positivity of energy and occurrence of naked singularity.     

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.     

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.     

Strong curvature naked singularities in non-self-similar gravitational collapse

It is shown that strong curvature naked singularities form in a non-self-similar gravitational collapse of radiation. The imploding radiation space-times with a general form of mass function are analyzed and we show that a strong curvature property holds along all families of non-spacelike geodesies terminating at the singularity in past. In view of the strength of singularity and the non-self-similar nature of space-time, we believe this is a very serious counter-example which must be taken into account for any possible formulation of the cosmic censorship hypothesis.This essay received the fourth award from the Gravity Research Foundation, 1991 — Ed.     

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.     

Null Fluid Collapse in Rastall Theory of Gravity

A Vaidya spacetime is considered for gravitational collapse of a type II fluid in the context of the Rastall theory of gravity. For a linear equation of state for the fluid profiles, the conditions under which the dynamical evolution of the collapse can give rise to the formation of a naked singularity are examined. It is shown that depending on the model parameters, strong curvature, naked singularities would arise as exact solutions to the Rastall's field equations. The allowed values of these parameters satisfy certain conditions on the physical reliability, nakedness, and the curvature strength of the singularity. It turns out that Rastall gravity, in comparison to general relativity, provides a wider class of physically reasonable spacetimes that admit both locally and globally naked singularities.     

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.     

Gravitational collapse: The story so far

An outstanding problem in gravitation theory and relativistic astrophysics today is to understand the final outcome of an endless gravitational collapse. Such a continual collapse would take place when stars more massive than few times the mass of the sun collapse under their own gravity on exhausting their nuclear fuel. According to the general theory of relativity, this results either in a black hole, or a naked singularity — which can communicate with far away observers in the universe. While black holes are (almost) being detected and are increasingly used to model high energy astrophysical phenomena, naked singularities have turned into a topic of active discussion, aimed at understanding their structure and implications. Recent developments here are reviewed, indicating future directions.     

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.     

Quasi-Spherical Gravitational Collapse in Any Dimension

We study the occurrence and nature of naked singularities for a dust model with non-zero cosmological constant in (n+2)-dimensional Szekeres space-times (which possess no Killing vectors) for n 2. We find that central shell-focusing singularities may be locally naked in higher dimensions but depend sensitively on the choice of initial data. In fact, the nature of the initial density determines the possibility of naked singularity in space-times with more than five dimensions. The results are similar to the collapse in spherically symmetric Tolman-Bondi-Lemaître space-times.     

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.     

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.     

Hawking Radiation as a Possible Probe for the Interior Structure of Regular Black Holes

The notion of black hole singularity and the proof of the singularity theorem were considered great successes in classical general relativity whereas they meanwhile brought with deep puzzles. Conceptual challenges were set up by the intractability of the singularity. The existence of black hole horizons which cover up the black hole interior including the singularity from outside observers, builds an information curtain, further hindering physicists from understanding the nature of the singularity and the interior structure of black holes. The regular black hole is a concept produced out of multiple attempts of establishing a tractable and understandable interior structure for black holes as well as avoiding the singularity behind the black hole horizon. The practicality of the new constructions of black holes would be considered more reliable if there can be found some connection between the interior of regular black holes and some far-reaching signals released from the black hole. After studying the Hawking radiation by fermion tunnelling from one type of regular black hole, structure dependent results were obtained. The result being structure dependent hints the prospects of employing the Hawking radiation as a method to probe into the structure of black holes.     

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.     

Effect of self-interaction on charged black hole radiance

We extend our previous analysis of the modification of the spectrum of black hole radiance due to the simplest and probably most quantitatively important back-reaction effect, that is self-gravitational interaction, to the case of charged holes. As anticipated, the corrections are small for low-energy radiation when the hole is well away from extremality, but become qualitatively important near extremality. A notable result is that radiation which could leave the hole with mass and charge characteristic of a naked singularity, predicted in the usual approximation of fixed space-time geometry, is here suppressed. We discuss the nature of our approximations, and show how they work in a simpler electromagnetic analogue problem.     

Acceleration of particles in Einstein-Maxwell-dilaton black holes

It has recently been pointed out that, under certain conditions, the energy of particles accelerated by black holes in the center-of-mass frame can become arbitrarily high. In this paper, we study the collision of two particles in the case of four-dimensional charged nonrotating, extremal charged rotating and near-extremal charged rotating Kaluza-Klein black holes as well as the naked singularity case in Einstein-Maxwell-dilaton theory. We find that the center-of-mass energy for a pair of colliding particles is unlimited at the horizon of charged nonrotating Kaluza-Klein black holes, extremal charged rotating Kaluza-Klein black holes and in the naked singularity case.     

Null charts and naked singularities in spherically symmetric,homothetic spacetimes

We give a unified derivation of a null chart for all spherically symmetric, homothetic spacetimes. These spacetimes contain an interesting class of naked singularities which we are also able to elucidate. Much use is made of graphical representation; in particular a chart of the spacetimes based on their homothetic group motions is introduced. Dust spacetimes, and two homogeneous examples with non-zero pressure (flat Robertson-Walker and a Kantowski-Sachs example) are studied in detail. We show the horizon structure in the null atlas, in comoving coordinates, in terms of the areal radius and comoving time, and in the homothetic diagrams. The critical delay between comoving observers for the onset of nakedness is interpreted in terms of a decreasing mass concentration in the spirit of Thorne's hoop conjecture. We also give a simple criterion for the existence of apparent horizons isolating the various singularities, and study in detail how this criterion is circumvented in the naked examples. We conclude that this type of naked singularity is a consequence of the imposed homothetic symmetry, by showing it to be generally present and timelike in the homothetic group chart even when it is not visible at comoving infinity (before the onset of criticality). It is the delayed final collapse of initially distant observers in inhomogeneous spacetimes that causes the initial singularity to become visible at comoving infinity. We conclude that these examples do not present an obstacle to the Event Horizon Conjecture as summarized by W. Israel (1984). That is, one can formulate criteria for the formation of apparent horizons that do not imply that all singularities are necessarily so enclosed. It is still possible that all singularities stronger than homothetic are isolated by an apparent horizon, in the spirit of Tipler's conjecture.On leave from Department of Physics, Queen's University, Kingston, Ontario, Canada     

Solving the hierarchy problem with noncompact extra dimensions

We show that gravitational effects of global cosmic 3-branes can be responsible for compactification from six to four space-time dimensions, naturally producing the observed hierarchy between electroweak and gravitational forces. The finite radius of the transverse dimensions follows from Einstein's equation, and is exponentially large compared with the scales associated with the 3-brane. The space-time ends on a mild naked singularity at the boundary of the transverse dimensions; nevertheless unitary boundary conditions render the singularity harmless.     

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.     

Orbiting naked singularities in large-$$\omega $$ Brans–Dicke gravity

Brans–Dicke gravity admits spherical solutions describing naked singularities rather than black holes. Depending on some parameters entering such a solution, stable circular orbits exist for all radii. One shows that, despite the fact a naked singularity is an infinite redshift location, the far observed orbital motion frequency is unbounded for an adiabatically decreasing radius. We then argue that this feature remains true in a wide set of scalar(s)–tensor theories if gravity. This is a salient difference with general relativity, and the repercussion on the gravitational radiation by EMRI systems is stressed. Since this behaviour survives the \(\omega \longrightarrow \infty \) limit, the possibility of such solutions is of utmost interest in the new gravitational wave astronomy context, despite the current constraints on scalar–tensor gravity.