Naked Singularity Case Research Articles

A rotating modified JNW spacetime as a Kerr black hole mimicker

AbstractThe Event Horizon Telescope has recently observed the images and shadows of the compact objects M87* and Sgr A* at the centres of the galaxies Messier 87 and Milky Way. This has opened up a new window in observational astronomy to probe and test gravity and fundamental physics in the strong-field regime. In this paper, we construct a rotating version of a modified Janis-Newman-Winicour metric obtained through the Simpson-Visser regularisation procedure and constrain the metric parameters using the observed shadows of M87* and Sgr A*. Depending on parameter values, the spacetime metric represents either a naked singularity or a wormhole. We find that the naked singularity case is not consistent with observations, as it casts a shadow that is much smaller than the observed ones. On the other hand, the shadow formed by the wormhole branch, depending on the parameter values, is consistent with the observations. We put constraints on the wormhole throat radius by comparing the shadow with the observed ones of M87* and Sgr A*.

Quantum-corrected rotating black holes and naked singularities in ( 2+1 ) dimensions

We analytically investigate the pertubative effects of a quantum conformally-coupled scalar field on rotating (2+1)-dimensional black holes and naked singularities. In both cases we obtain the quantum-backreacted metric analytically. In the black hole case, we explore the quantum corrections on different regions of relevance for a rotating black hole geometry. We find that the quantum effects lead to a growth of both the event horizon and the ergosphere, as well as to a reduction of the angular velocity compared to their corresponding unperturbed values. Quantum corrections also give rise to the formation of a curvature singularity at the Cauchy horizon and show no evidence of the appearance of a superradiant instability. In the naked singularity case, quantum effects lead to the formation of a horizon that hides the conical defect, thus turning it into a black hole. The fact that these effects occur not only for static but also for spinning geometries makes a strong case for the r\^ole of quantum mechanics as a cosmic censor in Nature.

Seeing relativity-II: Revisiting and visualizing the Reissner–Nordström metric

In this paper we study some features of the Reissner–Nordström metric both from an analytic and a visual point of view. We perform an accurate ray tracing and study of null geodesics in various situations. Among the issues we focus on are (i) the comparison with the Schwarzschild case, (ii) the naked singularity case, where, if the electric charge is not too large, some dark shell appears on images despite there is no horizon in the metric, and (iii) the wormhole crossing case, i.e. a visual exploration of the maximal analytic extension of the metric.

Intrinsic curvature and topology of shadows in Kerr spacetime

From the viewpoint of differential geometry and topology, we investigate the characterization of the shadows in a Kerr spacetime. Two new quantities, the length of the shadow boundary and the local curvature radius are introduced. Each shadow can be uniquely determined by these two quantities. For the black hole case, the result shows that we can constrain the black hole spin and the angular coordinate of the observer only by measuring the maximum and minimum of the curvature radius. While for the naked singularity case, we adopt the length parameter and the maximum of the curvature radius. This technique is completely independent of the coordinate system and the location of the shadow, and is expected to uniquely determine the parameters of the spacetime. Moreover, we propose a topological covariant quantity to measure and distinguish different topological structures of the shadows.

Acceleration of particles in Einstein-Maxwell-dilaton black holes**Supported by NSFC (11575202, 11205048), Foundation for Young Key Teacher of Henan Normal University and Cuiying Programme of Lanzhou University (225000-582404) and Fundamental Research Fund for Physics and Mathematic of Lanzhou University (LZULL200911)

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.

General classification of charged test particle circular orbits in Reissner\u2013Nordstr\xf6m spacetime

We investigate charged particles’ circular motion in the gravitational field of a charged mass distribution described by the Reissner–Nordström spacetime. We introduce a set of independent parameters completely characterizing the different spatial regions in which circular motion is allowed. We provide a most complete classification of circular orbits for different sets of particle and source charge-to-mass ratios. We study both black holes and naked singularities and show that the behavior of charged particles depend drastically on the type of source. Our analysis shows in an alternative manner that the behavior of circular orbits can in principle be used to distinguish between black holes and naked singularities. From this analysis, special limiting values for the dimensionless charge of black hole and naked singularity emerge, namely, Q/M = 1/2, Q/M=sqrt{13}/5 and Q/M=sqrt{2/3} for the black hole case and Q/M = 1, Q/M=5/ (2 sqrt{6}), Q/M=3 sqrt{6}/7, and finally Q/M= sqrt{9/8} for the naked singularity case. Similarly and surprisingly, analogous limits emerge for the orbiting particles charge-to-mass ratio epsilon , for positive charges epsilon =1, epsilon =2 and epsilon =M/Q. These limits play an important role in the study of the coupled electromagnetic and gravitational interactions, and the investigation of the role of the charge in the gravitational collapse of compact objects.

Spin precession in a black hole and naked singularity spacetimes

We propose here a specific criterion to address the existence or otherwise of Kerr naked singularities, in terms of the precession of the spin of a test gyroscope due to the frame dragging by the central spinning body. We show that there is indeed an important characteristic difference in the behavior of gyro spin precession frequency in the limit of approach to these compact objects, and this can be used, in principle, to differentiate the naked singularity from black hole. Specifically, if gyroscopes are fixed all along the polar axis upto the horizon of a Kerr black hole, the precession frequency becomes arbitrarily high, blowing up as the event horizon is approached. On the other hand, in the case of naked singularity, this frequency remains always finite and well-behaved. Interestingly, this behavior is intimately related to and is governed by the geometry of the ergoregion in each of these cases which we analyze here. One intriguing behavior that emerges is, in the Kerr naked singularity case, the Lense-Thirring precession frequency ($\Omega_{\rm LT}$) of the gyroscope due to frame-dragging effect decreases as ($\Omega_{\rm LT}\propto r$) after reaching a maximum, in the limit of $r= 0$, as opposed to $r^{-3}$ dependence in all other known astrophysical cases.

Superradiance initiated inside the ergoregion

We consider the stationary metrics that have both the black hole and the ergoregion. The class of such metric contains, in particular, the Kerr metric. We study the Cauchy problem with highly oscillatory initial data supported in a neighborhood inside the ergoregion with some initial energy [Formula: see text]. We prove that when the time variable [Formula: see text] increases this solution splits into two parts: one with the negative energy [Formula: see text] ending at the event horizon in a finite time, and the second part, with the energy [Formula: see text], escaping, under some conditions, to the infinity when [Formula: see text]. Thus we get the superradiance phenomenon. In the case of the Kerr metric the superradiance phenomenon is “short-lived”, since both the solutions with positive and negative energies cross the outer event horizon in a finite time (modulo [Formula: see text]) where [Formula: see text] is a large parameter. We show that these solutions end on the singularity ring in a finite time. We study also the case of naked singularity.

Shadow of a naked singularity

We analyze the redshift suffered by photons originating from an external source, traversing a collapsing dust cloud and finally being received by an asymptotic observer. In addition, we study the shadow that the collapsing cloud casts on the sky of the asymptotic observer. We find that the resulting redshift and properties of the shadow depend crucially on whether the final outcome of the complete gravitational collapse is a black hole or a naked singularity. In the black hole case, the shadow is due to the high redshift acquired by the photons as they approach the event horizon, implying that their energy is gradually redshifted toward zero within a few crossing times associated with the event horizon radius. In contrast to this, a naked singularity not only absorbs photons originating from the source, but it also emits infinitely redshifted photons with and without angular momenta. This emission introduces an abrupt cutoff in the frequency shift of the photons detected in directions close to the radial one, and it is responsible for the shadow masking the source in the naked singularity case. Furthermore, even though the shadow forms and begins to grow immediately after the observer crosses the Cauchy horizon, it takes many more crossing times than in the black hole case for the source to be occulted from the observer's eyes. We discuss possible implications of our results for testing the weak cosmic censorship hypothesis. Even though at late times the image of the source perceived by the observer looks the same in both cases, the dynamical formation of the shadow and the redshift images has distinct features and time scales in the black hole versus the naked singularity case. For stellar collapse, these time scales seem to be too short to be resolved with existing technology. However, our results may be relevant for the collapse of seeds leading to supermassive black holes.

The ergoregion in the Kerr spacetime: properties of the equatorial circular motion

We investigate in detail the circular motion of test particles in the equatorial plane of the ergoregion in the Kerr spacetime. We consider all the regions where circular motion is allowed, and we analyze the stability properties and the energy and angular momentum of the test particles. We show that the structure of the stability regions has definite features that make it possible to distinguish between black holes and naked singularities. The naked singularity case presents a very structured non-connected set of regions of orbital stability, where the presence of counterrotating particles and zero angular momentum particles for a specific class of naked singularities is interpreted as due to the presence of a repulsive field generated by the central source of gravity. In particular, we analyze the effects of the dynamical structure of the ergoregion (the union of the orbital regions for different attractor spins) on the behavior of accretion disks around the central source. The properties of the circular motion turn out to be so distinctive that they allow for the introduction of a complete classification of Kerr spacetimes, each class of which is characterized by different physical effects that could be of especial relevance in observational astrophysics. We also identify some special black-hole spacetimes where these effects could be relevant.

Weak and strong field approximations and circular orbits of the Kehagias‐Sfetsos space‐time

AbstractThe Kehagias‐Sfetsos asymptotically flat black hole and naked singularity solutions of the Hořava‐Lifshitz gravity are investigated both in the weak‐field and strong‐field regimes. In the weak‐field limit the gravitational field generated by the Kehagias‐Sfetsos spherically symmetric solution is weaker then in the case of the Schwarzschild black hole of general relativity. In the strong‐field regime naked singularities with ω0 ≪ 1 display an unusual distance dependence: gravity becomes weaker when approaching the singularity. The stability of circular orbits is also analyzed. While in the black hole case the square of the angular momentum should be larger than a certain finite, non‐zero minimal value, in the naked singularity case there are stable circular orbits for any non‐zero value of the angular momentum. In this regime we prove the existence of an infimum of the allowed radii of circular orbits (corresponding to vanishing angular momentum). (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

CHARGED MEMBRANE AS A SOURCE FOR REPULSIVE GRAVITY

We demonstrate an alternative (with respect to the ones existing in the literature) and more-typical-for-physicists derivation of an exact solution to the Einstein–Maxwell equations for the motion of a charged spherical membrane with tangential tension. We stress that there exists physically acceptable range of parameters for which the static and stable state of the membrane producing the Reissner–Nordstrom (RN) repulsive gravity effect exists. The concrete realization of such a state for the Nambu–Goto membrane is described. The point is that the membrane is able to cut out the central naked singularity region and at the same time join in an appropriate way the RN repulsive region. As a result we have a model of an everywhere-regular material source exhibiting a repulsive gravitational force in the vicinity of its surface: this construction gives a more sensible physical status to the RN solution in the naked singularity case.

Photon trajectories in the Kerr-Newman metric

Gives a detailed description of the null trajectories in the Kerr-Newman metric. Interesting results which were not expected from what was known in the uncharged case are a considerable enhancement of the energy storage in a restricted region around the source in the naked singularity case and the singularity is completely disconnected from the asymptotic region in the sense that no photon can reach it even in the equatorial plane.