We study bound orbits near the centres of static, spherically symmetric, asymptotically flat configurations of a self-gravitating scalar field minimally coupled to gravity. In our approach, a nonlinear scalar field is considered as an idealized model of dark matter, and the main examples that we have in mind are the centres of galaxies. We consider both scalar field black holes (SFBHs) and scalar field naked singularities (SFNSs). It turns out that the shape and parameters of a bound orbit depend crucially on the type of configuration. The lapse metric function of a SFNS and, consequently, the effective potential of a massive test particle with zero angular momentum have a global minimum. A SFNS has a static degenerated orbit on which a test particle, having zero angular momentum and the minimum of its energy, remains at rest at all times. This implies that there exists a spherical shell consisting of cold gas or dust, which for a distant observer can look like the shadow of a black hole. We also study the shape of noncircular bound orbits close to the centres of SFNSs and show that their angles of precession are negative.
Repulsive gravity is a well known characteristic of naked singularities. In this work, we explore light surfaces and find new effects of repulsive gravity. We compare Kerr naked singularities with the corresponding black hole counterparts and find certain structures that are identified as horizon remnants. We argue that these features might be significant for the comprehension of processes that lead to the formation or eventually destruction of black hole Killing horizons. These features can be detected by observing photon orbits, particularly close to the rotation axis, which can be used to d…
We study the linear polarization from the accretion disk around weakly and strongly naked Janis-Newman-Winicour singularities. We consider an analytical toy model of thin magnetized fluid ring orbiting in the equatorial plane and emitting synchrotron radiation. The observable polarized images are calculated and compared to the Schwarzschild black hole for physical parameters compatible with the radio source M87. For small inclination angles the direct images of the weakly naked singularities closely mimic the Schwarzschild black hole. The deviation in the polarization properties increases if w…
We construct perfect fluid tori in the field of the Kehagias-Sfetsos (K-S) naked singularity representing spherically symmetric vacuum solution of the modified Hořava quantum gravity that is characterized by a dimensionless parameter $ωM^2$, combining the gravitational mass parameter $M$ of the spacetime with the Hořava parameter $ω$ reflecting the role of the quantum corrections. In dependence on the value of $ωM^2$, the K-S naked singularities demonstrate a variety of qualitatively different behavior of their circular geodesics that is fully reflected in the properties of the toroidal struct…
Naked singularities are hypothetical astrophysical objects, characterized by a gravitational singularity without an event horizon. Penrose has proposed a conjecture, according to which there exists a cosmic censor who forbids the occurrence of naked singularities. Distinguishing between astrophysical black holes and naked singularities is a major challenge for present day observational astronomy. A possibility of differentiating naked singularities from black holes is through the comparative study of thin accretion disks properties around rotating naked singularities and Kerr-type black holes,…
We study the properties of black holes and naked singularities by considering stationary observers and light surfaces in Kerr spacetimes. We reconsider the notion of Killing horizons from a special perspective by exploring the entire family of Kerr metrics. To this end, we introduce the concepts of extended plane, Killing throats and bottlenecks for weak (slowly spinning) naked singularities. Killing bottlenecks (or horizon remnants in analogy with the corresponding definition of throats in black holes) are restrictions of the Killing throats appearing in special classes of slowly spinning nak…
For a wide class of spherically symmetric naked singularities there is a sphere within which gravity is effectively repulsive. In such spacetimes accreting matter cannot reach the singularity and will instead form a levitating atmosphere, which is kept suspended by gravity alone. The density of the atmosphere has a maximum at a definite radius. In its qualitative properties the atmosphere is analogous to the recently discussed atmospheres that are supported by radiation pressure above luminous neutron stars, however for the levitating atmospheres around a naked singularity no radiation need be…
We formulate a generic Newtonian like analogous potential for static spherically symmetric general relativistic (GR) spacetime, and subsequently derived proper Newtonian like analogous potential corresponding to Janis-Newman-Winicour (JNW) and Reissner-Nordström (RN) spacetimes, both exhibiting naked singularities. The derived potentials found to reproduce the entire GR features including the orbital dynamics of the test particle motion and the orbital trajectories, with precise accuracy. The nature of the particle orbital dynamics including their trajectory profiles in JNW and RN geometries s…
We study here images of thin accretion disks around black holes and two classes of naked singularity spacetimes and compare these scenarios. The naked singularity models which have photon spheres have single accretion disk with its inner edge lying outside the photon sphere. The images and shadows created by these models mimic those of black holes. It follows, therefore, that further and more detailed analysis of the images and shadows structure in such case is needed to confirm or otherwise the existence of an event horizon for the compact objects such as the galactic centers. However, naked …
We generalize here our earlier results on particle acceleration by naked singularities. We showed recently[1] that the naked singularities that form due to gravitational collapse of massive stars provide a suitable environment where particles could get accelerated and collide at arbitrarily high center of mass energies. However, we focussed there only on the spherically symmetric gravitational collapse models, which were also assumed to be self-similar. In this paper, we broaden and generalize the result to all gravitational collapse models leading to the formation of a naked singularity as fi…
It is commonly thought that the final product of gravitational collapse is a black hole. Nevertheless, theoretical studies have not yet provided a final answer to the question whether black holes are the only possible outcome or whether naked singularities are also allowed. Observational tests may thus represent a complementary approach. In the present paper, we consider the Janis-Newman-Winicour metric, which describes a rotating source with a surface-like naked singularity. We calculate iron line shapes in the reflection spectrum of a putative disk around a Janis-Newman-Winicour singularity …
We comment here on the results in Ref [4] that showed naked singularities in dynamical gravitational collapse of inhomogeneous dust to be stable but non-generic. The definition of genericity used there is reconsidered. We point out that genericity in terms of an open set, with a positive measure defined suitably on the space of initial data, is physically more appropriate compared to the dynamical systems theory definition used in [4] which makes both black holes and naked singularities non-generic as collapse outcomes.
We discuss photon and test-particle orbits in the Kehagias-Sfetsos (KS) metric. For any value of the Hořava parameter $ω$, there are values of the gravitational mass $M$ for which the metric describes a naked singularity, and this is always accompanied by a vacuum "antigravity sphere" on whose surface a test particle can remain at rest (in a zero angular momentum geodesic), and inside which no circular geodesics exist. The observational appearance of an accreting KS naked singularity in a binary system would be that of a quasi-static spherical fluid shell surrounded by an accretion disk, whose…
Proceedings of the second edition of the international Workshop "Dynamics and Thermodynamics of Blackholes and Naked Singularities" (Department of Mathematics of the Politecnico of Milano from May 10-12, 2007.
Proceedings of the international Workshop on ``Dynamics and Thermodynamics of Blackholes and Naked Singularities``, that took place at the Department of Mathematics of the Politecnico of Milano from 13 to 15 May 2004.
We investigate the occurrence of naked singularities in the spherically symmetric, plane symmetric and cylindrically symmetric collapse of charged null fluid in an anti-de Sitter background. The naked singularities are found to be strong in Tipler's sense and thus violate the cosmic censorship conjecture, but not hoop conjecture.
Solutions describing the gravitational collapse of asymptotically flat cylindrical and prolate shells of (null) dust are shown to admit globally naked singularities.
In this paper, we derive general conditions for a shadow to occur, without a photon sphere in a spacetime, caused by central nulllike or timelike naked singularities. Using these conditions, we propose classes of spacetimes which have nulllike and timelike naked singularities at the center, and that fulfill these `shadow without photon sphere' conditions. Considering additional asymptotically flat conditions, we show that, for a fixed Schwarzschild mass, the timelike naked singularities can cast a shadow of a size that is equal to, greater or smaller, than the size of a black hole shadow. On t…
We investigate the gravitational field of a static mass with quadrupole moment in empty space. It is shown that in general this configuration is characterized by the presence of curvature singularities without a surrounding event horizon. These naked singularities generate an effective field of repulsive gravity which, in turn, drastically changes the behavior of test particles. As a possible consequence, the accretion disk around a naked singularity presents a particular discontinuous structure.
In this work we study collapse of a general matter in a most general spacetime i.e., a spacetime with any matter and without (assuming) any symmetry. We show that the energy is completely trapped inside the null singularity and therefore they cannot be experimentally observed. This most general result implies, there is no physical significance of the null naked singularities irrespective of their existence. This conclusion strongly supports the essence of cosmic censorship hypothesis.
We investigate here the particle acceleration by naked singularities to arbitrarily high center of mass energies. Recently it has been suggested that black holes could be used as particle accelerators to probe the Planck scale physics. We show that the naked singularities serve the same purpose and probably would do better than their black hole counterparts. We focus on the scenario of a self-similar gravitational collapse starting from a regular initial data, leading to the formation of a globally naked singularity. It is seen that when particles moving along timelike geodesics interact and c…
We study an analytical solution to the Einstein's equations in 2+1-dimensions, representing the self-similar collapse of a circularly symmetric, minimally coupled, massless, scalar field. Depending on the value of certain parameters, this solution represents the formation of naked singularities. Since our solution is asymptotically flat, these naked singularities may be relevant for the weak cosmic censorship conjecture in 2+1-dimensions.
We study the occurrence of naked singularities in the spherically symmetric collapse of a charged null fluid in an expanding deSitter background - a piece of charged Vaidya-deSitter spacetime. The necessary conditions for the formation of a naked singularity are found. The results for the uncharged solutions can be recovered from our analysis.
We investigate the occurrence and nature of a naked singularity in the gravitational collapse of an inhomogeneous dust cloud described by a non self-similar higher dimensional Tolman spacetime. The necessary condition for the formation of a naked singularity or a black hole is obtained. The naked singularities are found to be gravitationally strong in the sense of Tipler and provide another example that violates the cosmic censorship conjecture.
We show that the behaviour of outgoing radial null geodesic congruence on the apparent horizon is related to the property of nakedness in spherical dust collapse justifying the difference between the Penrose diagrams in the naked and covered dust collapse scenarios. We provide arguments suggesting that the relationship could be generally valid.
Global visibility of naked singularities is analyzed here for a class of spherically symmetric spacetimes, extending previous studies - limited to inhomogeneous dust cloud collapse - to more physical valid situations in which pressures are non-vanishing. Existence of nonradial geodesics escaping from the singularity is shown, and the observability of the singularity from far-away observers is discussed.
We investigate the occurrence and nature of naked singularities in the Szekeres space-times. These space-times represent irrotational dust. They do not have any Killing vectors and they are generalisations of the Tolman-Bondi-Lemaitre space-times. It is shown that in these space-times there exist naked singularities that satisfy both the limiting focusing condition and the strong limiting focusing condition. The implications of this result for the cosmic censorship hypothesis are discussed.
In order to show that there exists a relation between the validity of the Weyl entropy and the cosmic censorship hypothesis, we discuss the relation between naked singularities and the gravitational entropy estimator using the Weyl invariant. We look at the examples of Vaidya and Tolman-Bondi spacetimes in asymptotically flat and de Sitter spacetime and look at Weyl entropy as a possible indicator of the prohibition of naked singularities.
We show that the behaviour of the outgoing radial null geodesic congruence on the boundary of the trapped region (suitably defined as a four dimensional region) is related to the property of nakedness in spherical dust collapse. The argument involves a conformal transformation which justifies the difference in the Penrose diagrams in the naked and covered dust collapse scenarios.
We investigate the end state of gravitational collapse of null fluid in higher dimensional space-times. Both naked singularities and black holes are shown to be developing as final outcome of the collapse. The naked singularity spectrum in collapsing Vaidya region (4D) gets covered with increase in dimensions and hence higher dimensions favor black hole in comparison to naked singularity. The Cosmic Censorship Conjecture will be fully respected for a space of infinite dimension.
We show that all known naked singularities in spherically symmetric self-similar spacetimes arise as a result of singular initial matter distribution. This is a result of the peculiarity of the coordinate transformation that takes these spacetimes into a separable form. Therefore, these examples of naked singularities are of no apparent consequence to astrophysical observations or theories.
A new mechanism for causing naked singularities is found in an effective superstring theory. We investigate the gravitational collapse in a spherically symmetric Einstein-Maxwell-dilaton system in the presence of a pure cosmological constant "potential", where the system has no static black hole solution. We show that once gravitational collapse occurs in the system, naked singularities necessarily appear in the sense that the field equations break down in the domain of outer communications. This suggests that in generalized theories of gravity, the non-minimally coupled fields generically cau…
In this paper we study the Hawking radiation in Reissner-Nordstrom and Kerr-Newman black holes by considering the charge to be the function of radial coordinate.
We show that the black hole solutions of the effective string theory action, where one-loop effects that couple the moduli to gravity via a Gauss-Bonnet term are taken into account, admit primary scalar hair. The requirement of absence of naked singularities imposes an upper bound on the scalar charges.
We study the formation of central naked singularities in spherical dust collapse with a cosmological constant. We find that the central curvature singularity is locally naked, Tipler strong, and generic, in the sense that it forms from a non-zero-measure set of regular initial data. We also find that the Weyl and Ricci curvature scalars diverge at the singularity, with the former dominating over the latter, thereby signaling the non-local origin of the singularity.
Following recent literature on dS instability in presence of interactions, we study the decay of massive particles in general FRW models and the emission from naked singularities either associated with 4D charged black holes or with 2D shock waves, by means of the Hamilton--Jacobi tunneling method. It is shown that the two-dimensional semi-classical tunneling amplitude from a naked singularity computed in that way is the same as the one-loop result of quantum field theory.
Continued gravitational collapse gives rise to curvature singularities. If a curvature singularity is globally naked then the space-time may be causally future ill-behaved admitting closed time-like or null curves which extend to asymptotic distances and generate a Cosmic Time Machine (de Felice (1995) Lecture Notes in Physics 455, 99). The conjecture that Cosmic Time Machines give rise to high energy impulsive events is here considered in more details.
We investigate here the genericity and stability aspects for naked singularities and black holes that arise as the final states for a complete gravitational collapse of a spherical massive matter cloud. The form of the matter considered is a general Type I matter field, which includes most of the physically reasonable matter fields such as dust, perfect fluids and such other physically interesting forms of matter widely used in gravitation theory. We first study here in some detail the effects of small pressure perturbations in an otherwise pressure-free collapse scenario, and examine how a co…
We model massive compact objects in galactic nuclei as stationary, axially-symmetric naked singularities in the Einstein-massless scalar field theory and study the resulting gravitational lensing. In the weak deflection limit we study analytically the position of the two weak field images, the corresponding signed and absolute magnifications as well as the centroid up to post-Newtonian order. We show that there are a static post-Newtonian corrections to the signed magnification and their sum as well as to the critical curves, which are function of the scalar charge. The shift of the critical c…
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 is one of the most striking phenomena in gravitational physics. The cosmic censorship conjecture has provided strong motivation for researches in this field. In the absence of general proof for the censorship, many examples have been proposed, in which naked singularity is the outcome of gravitational collapse. Recent development has 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'',…
Both the static and homogeneous metrics describing the spherically symmetric gravitational field of a crossflow of incoming and outgoing null dust streams are generalized for the case of the two-component ghost radiation. Static solutions represent either naked singularities or the wormholes recently found by Hayward. The critical value of the parameter separating the two possibilities is given. The wormhole is allowed to have positive mass. The homogeneous solutions are open universes.
Spherically symmetric inhomogeneous dust collapse has been studied in higher dimensional space-time and the factors responsible for the appearance of a naked singularity are analyzed in the region close to the centre for the marginally bound case. It is clearly demonstrated that in the former case naked singularities do not appear in the space-time having more than five dimension, which appears to a strong result. The non-marginally bound collapse is also examined in five dimensions and the role of shear in developing naked singularities in this space-time is discussed in details. The five dim…
Gravitational collapse of a spherically symmetric cloud has been extensively studied to investigate the nature of resulting singularity. However, there has been considerable debate about the admissibility of certain initial density distributions. Using the Newtonian limit of the equations governing collapse of a fluid with an equation of state $p=p(ρ)$ it is shown that the density distribution has to be even function of r in a spherically symmetric situation provided $dp/dρ\ne0$. Implications of this result on formation of strong naked singularities are examined.
We discuss stationary supersymmetric bosonic configurations of the Einstein-Maxwell theory embedded in $N=2$ supergravity. Some of these configurations, including the Kerr-Newman solutions with $m = |q|$ and arbitrary angular momentum per unit mass $a$, exhibit naked singularities. However, $N=2$ supergravity has trace anomaly. The nonvanishing anomalous energy-momentum tensor of these Kerr-Newman solutions violates a consistency condition for a configuration to admit unbroken supersymmetry. Thus, the trace anomaly of this theory prevents the supersymmetric solutions from exhibiting naked sing…
We consider the question here whether the proposed electromagnetic counterpart of the gravitational wave signals in binary black hole coalescence may be due to the appearance of a `short lived' naked singularity during the merger. We point out that the change in topology that the spacetime undergoes during the merger can cause the appearance of a naked singularity. In case some matter, in the form of a small accretion disk, is present in the surroundings of the black hole system then the emitted luminosity during the merger would allow to distinguish the scenario where the naked singularity fo…
In this paper, we will investigate the consequences of loop quantum gravitational modifications on the formation of naked singularities. The loop quantum gravitational effects will be incorporated in the collapsing system using gravity's rainbow. This will be done by using rainbow functions, which are constructed from loop quantum gravitational modifications to the energy momentum dispersion. It will be observed that this modification will prevent the formation of naked singularity. Thus, such a modification can ensures that the weak cosmic censorship hypothesis will hold for any collapsing sy…
We investigate the existence of repulsive gravitational acceleration near naked singularities. The investigation is carried out by means of the acceleration tensor, which is a coordinate invariant object. We find that the gravitational acceleration is repulsive in the vicinity of the origin in the Reissner-Nordstrøm and in the Kerr space-times, and attractive at large distances in the expected Newtonian way. We further address the space-time of a point massive particle, which also exhibits repulsive effects near the origin.
We investigate the occurrence of naked singularities, local and global, in the incoming Vaidya spacetimes with zero initial mass. While it is well-known that these spacetimes admit locally and globally naked singularities, we demonstrate that globally naked singularities are significantly more common than is stressed in the literature, being generic in a natural topology on this collection of spacetimes. A heuristic consequence of the results is that the slow accumulation of mass is both necessary and sufficient for both types of naked singularities in these spacetimes. We demonstrate that the…
We investigate thermodynamic properties of two types of asymptotically anti-de Sitter spacetimes: black holes and singular scalar field spacetimes. We describe the possibility that thermodynamic phase transitions can transform one spacetime into another, suggesting that black holes can radiate to naked singularities.
Gamma-ray bursts are believed to be the most luminous objects in the Universe. There has been some suggestion that these arise from quantum processes around naked singularities. The main problem with this suggestion is that all known examples of naked singularities are massless and hence there is effectively no source of energy. It is argued that a globally naked singularity coupled with quantum processes operating within a distance of the order of Planck length of the singularity will probably yield energy burst of the order of M_pc^2\approx2\times 10^{16} ergs, where M_p is the Planck mass.
