A Kerr black hole with mass parameter m and angular momentum parameter a acting as a gravitational lens gives rise to two images in the weak field limit. We study the corresponding magnification relations, namely the signed and absolute magnification sums and the centroid up to post-Newtonian order. We show that there are post-Newtonian corrections to the total absolute magnification and centroid proportional to a/m, which is in contrast to the spherically symmetric case where such corrections vanish. Hence we also propose a new set of lensing observables for the two images involving these corrections, which should allow measuring a/m with gravitational lensing. In fact, the resolution capabilities needed to observe this for the Galactic black hole should in principle be accessible to current and near-future instrumentation. Since a/m >1 indicates a naked singularity, a most interesting application would be a test of the Cosmic Censorship conjecture. The technique used to derive the image properties is based on the degeneracy of the Kerr lens and a suitably displaced Schwarzschild lens at post-Newtonian order. A simple physical explanation for this degeneracy is also given.
We check the weak cosmic censorship conjecture by attempting to overspin the Kerr-Newman-Kasuya black hole with test particle. The study suggests that the Kerr-Newman-Kasuya black hole can be over-spun showing the violation of cosmic censorship conjecture.
It has been suggested by Israel that the Kerr singularity cannot be strong in the sense of Tipler, for it tends to cause repulsive effects. We show here that, contrary to that suggestion, nearly all null geodesics reaching this singularity do in fact terminate in Tipler's strong curvature singularity. Implications of this result are discussed in the context of an earlier cosmic censorship theorem which constraints the occurrence of Kerr-like naked singularities in generic collapse situations.
According to the cosmic censorship hypothesis of Penrose, naked singularities should never occur in realistic collapse situations. One of the major open problems in this context is the existence of a naked singularity in the Kerr solution with |a|>m; this singularity can be interpreted as the final product of collapse of a rapidly rotating object. Assuming that certain very general and physically reasonable conditions hold, we show here, using the global techniques, that a realistic gravitational collapse of any rotating object, which develops from a regular initial state, cannot lead to the f…
Using some probes, the violation of cosmic censorship conjecture in a general Kerr-Newman black hole is investigated. The result depends on many factors, like the relative sign of charge and rotation direction of the probe and black hole. Moreover the comparison of the angular momentum of the black hole and its charge has an impressive effect. Considering all these together, we have found the range of the angular momentum, energy and charge of the probe for which the event horizon disappears. We have found that cosmic censorship conjecture violation is possible only for near extremal black hol…
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.
We first calculate equations of motion for particles in the Kerr-Sen-de Sitter black hole spacetime. Then in the eikonal regime, we analytically obtain the quasi-normal resonant modes of massless neutral scalar field perturbation and find its imaginary part to be characterized by the surface gravity of the near-extremal Kerr-Sen-de Sitter black hole with Cauchy horizon approaching the event horizon. We further show that the Penrose strong cosmic censorship conjecture is thus respected in this spacetime with dilaton scalar field and axion pseudoscalar field.
It has been shown previously that an extremal Reissner-Nordström or an extremal Kerr black hole cannot be overcharged or overspun by a test particle if radiative and self-force effects are neglected. In this paper, we consider extremal charged and rotating black holes with cosmological constants. By studying the motion of test particles, we find the following results: An extremal Reissner-Nordström anti-de Sitter (RN-AdS) black hole can be overcharged by a test particle but an extremal Reissner-Nordström de Sitter (RN-dS) black hole cannot be overcharged. We also show that both extrmal Kerr-de…
We investigate the weak cosmic censorship conjecture for Kerr-Sen black holes, which are solutions to the four-dimensional low-energy effective field theory for the heterotic string theory, based on the scattering of a charged scalar field. When the fluxes of the scalar field are assumed to transfer its conserved quantities to the black hole, extremal and near-extremal black holes cannot be over-spun and over-charged in their first-order variations, which is sufficient to conclude that the weak cosmic censorship conjecture is valid for Kerr-Sen black holes. We confirm our conclusion by relatin…
We show that cosmic censorship takes an exceptionally complex and interesting form in the case of five-dimensional AdS-Kerr black holes, due to the unusually distant relation obtaining in that case between the black hole parameters and the physical mass and angular momentum. One finds that, in this case, censorship is less restrictive than one might hope: it apparently allows some rather bizarre behaviour, and in particular does not prohibit arbitrarily large angular momenta. We find however that most of the unwelcome geometries permitted by censorship can be eliminated by requiring stability …
Motivated by the recent researches of black holes with NUT charge, we investigate the validity of the weak cosmic censorship conjecture for Kerr-Taub-NUT black hole with a test massive scalar field and a test particle, respectively. For the scalar field scattering gedanken experiment, we consider an infinitesimal time interval process. The result shows that both extremal and near-extremal Kerr-Taub-NUT black holes cannot be over-spun. For the test particle thought experiment, the study suggests that extremal Kerr-Taub-NUT black hole cannot be over-spun; while near-extremal Kerr-Taub-NUT black …
In this paper, we investigate the Weak Cosmic Censorship Conjecture in nearly extremal Kerr black hole by absorbing particles . In previous work, they ignore the process of black hole absorbing particles. They assume the whole particle can be absorbed and the overspinning occurs. However, it is questionable whether the whole particle can be absorbed. Therefore, we will investigate it in this paper. We consider the absorption process of a particle with finite size. During this absorption process, the black hole's parameters will change. This change will prevent the rest part of particle enter b…
We investigate the weak cosmic censorship conjecture in extremal and near-extremal Kerr-Newman-(anti-)de Sitter black holes by the scattering of a massive scalar field with an electric charge. Under this scattering, the scalar field fluxes change the black hole state, as determined by the mass, angular momentum, and electric charge. The black hole may exceed its extremal condition because of these changes. However, we find that the black hole cannot be overcharged or overspun by the scattering. In particular, although the fluxes are closely associated with the asymptotic boundary conditions al…
According to the Cosmic Censorship Conjecture, all the singularities produced by the collapsing matter must be hidden behind an event horizon. In 4D general relativity, this implies that the final product of the collapse is a Kerr-Newman black hole. Here I consider the possibility that the Cosmic Censorship Conjecture can be violated. I present the results of some numerical simulations of the accretion process onto Kerr black holes (objects with event horizon) and Kerr super-spinars (fast-rotating objects without event horizon). This is a preliminary study to investigate how the Cosmic Censors…
We investigate the laws of thermodynamics and weak cosmic censorship conjecture in the normal and extended phase space of a Kerr-AdS black hole by analyzing the energy-momentum relation of the absorbed fermion dropping into the horizon. In the normal phase space, the first law, second law as well as the weak cosmic censorship conjecture are found to be valid in all the initial states of the black hole. However, in the extended phase space, although the first law and weak cosmic censorship conjecture are still valid, the second law becomes more subtle. We find that the validity or violation of …
By neglecting the effects of self-force and radiation, we investigate the possibility of destroying the Kerr-MOG black hole through the point particle absorption process. Using the instability of event horizon and equation of particle motion, we get the upper and lower energy bounds allowed for a matter particle to produce the naked singularity. We find that the energy gap always exists between the upper and lower energy bounds for both extremal and near-extremal black holes, which means some tailored particles can actually lead to the violation of the weak cosmic censorship conjecture. Howeve…
A thought experiment considered recently in the literature, in which it is investigated whether a dyonic Kerr-Newman black hole can be destroyed by overcharging or overspinning it past extremality by a massive complex scalar test field, is revisited. Another derivation of the result that this is not possible, i.e. the weak cosmic censorship is not violated in this thought experiment, is given. The derivation is based on conservation laws, on a null energy condition, and on specific properties of the metric and the electromagnetic field of dyonic Kerr-Newman black holes. The metric is kept fixe…
Recent work has argued that the strong cosmic censorship (SCC) conjecture is violated by near-extremal Reissner-Nordström de Sitter (RNdS) black holes but respected by Kerr-de Sitter black holes. It has also been shown that the conjecture is violated by near-extremal BTZ black holes. The latter result relies on a coincidence between "exterior" and "interior" quasinormal frequencies. If this coincidence were to occur also for RNdS or Kerr-dS then it would significantly modify the conclusions of earlier work. In this paper, it is demonstrated that this coincidence does not occur for RNdS or Kerr…
We construct a gedanken experiment in which an extremal Kerr black hole interacts with a test electromagnetic field. Using Teukolsky's solutions for electromagnetic perturbations in Kerr spacetime, and the conservation laws imposed by the energy momentum tensor of the electromagnetic field and the Killing vectors of the spacetime, we prove that this interaction cannot convert the black hole into a naked singularity, thus cosmic censorship conjecture is not violated in this case.
A strongly naked singularity (SNS) was modelled at the center of the Galaxy. This specific type of naked singularity was characterized in 2008 by Virbhadra and Keeton. The lens is described using the Janis-Newman-Winicour metric, which has an ordinary mass and massless scalar charge parameters. Gravitational lensing by the SNS gives rise to 4 images: 2 images on the same side as the source and 2 images on the opposite side of the source from the optic axis. We compute magnification centroid, magnification centroid shift, and total absolute magnification for many values of the angular source po…
Precise late-time asymptotics of scalar field in the interior of a subextreme Kerr black hole and its application in Strong Cosmic Censorship conjecture
We test the weak cosmic censorship conjecture for magnetized Kerr-Newman spacetime via the method of injecting a test particle. Hence, we need to know how the black hole's parameters change when a test particle enters the horizon. This was an unresolved issue for non-asymptotically flat spacetimes since there are ambiguities on the energies of black holes and particles. We find a novel approach to solve the problem. We start with the "physical process version" of the first law, which relates the particle's parameters with the change in the area of the black hole. By comparing this first law wi…
The validity of the cosmic censorship conjecture for the Kerr-Sen black hole, which is a solution to the low-energy effective field theory for four-dimensional heterotic string theory, is investigated using charged particle absorption. When the black hole absorbs the particle, the charge on it changes owing to the conserved quantities of the particle. Changes in the black hole are constrained to the equation for the motion of the particle and are consistent with the laws of thermodynamics. Particle absorption increases the mass of the Kerr-Sen black hole to more than that of the absorbed charg…
The quasinormal resonant modes of massless neutral fields in near-extremal Kerr-Newman-de Sitter black-hole spacetimes are calculated in the eikonal regime. It is explicitly proved that, in the angular momentum regime ${\bar a}> \sqrt{{1-2{\barΛ}\over{4+{\barΛ}/3}}}$, the black-hole spacetimes are characterized by slowly decaying resonant modes which are described by the compact formula $\Imω(n)=κ_+\cdot(n+{1\over2})$ [here the physical parameters $\{{\bar a},κ_+,{\barΛ},n\}$ are respectively the dimensionless angular momentum of the black hole, its characteristic surface gravity, the dimensio…
It was investigated recently, with the aim of testing the weak cosmic censorship conjecture, whether an extremal Kerr black hole can be converted into a naked singularity by interaction with a massless classical Dirac test field, and it was found that this is possible. We generalize this result to electrically and magnetically charged rotating extremal black holes (i.e. extremal dyonic Kerr-Newman black holes) and massive Dirac test fields, allowing magnetically or electrically uncharged or nonrotating black holes and the massless Dirac field as special cases. We show that the possibility of t…
We investigate the weak cosmic censorship conjecture in Kerr-(anti-)de Sitter black holes under the scattering of a scalar field. We test the conjecture in terms of whether the black hole can exceed the extremal condition with respect to its change caused by the energy and angular momentum fluxes of the scalar field. Without imposing the laws of thermodynamics, we prove that the conjecture is valid in all the initial states of the black hole (non-extremal, near-extremal, and extremal black holes). The validity in the case of the near-extremal black hole is different from the results of similar…
We develop a unified, analytic framework for gravitational lensing by Kerr black holes. In this first paper we present a new, general lens equation and magnification formula governing lensing by a compact object. Our lens equation assumes that the source and observer are in the asymptotically flat region and does not require a small angle approximation. Furthermore, it takes into account the displacement that occurs when the light ray's tangent lines at the source and observer do not meet on the lens plane. We then explore our lens equation in the case when the compact object is a Kerr black h…
It has been shown that a nearly extremal black hole can be overcharged or overspun by a test particle if radiative and self-force effects are neglected, indicating that the cosmic censorship might fail. In contrast, the existing evidence in literature suggests that an extremal black hole cannot be overcharged or overspun in a similar process. In this paper, we show explicitly that even an exactly extremal black hole can be destroyed by a test particle, leading to a possible violation of the cosmic censorship. By considering higher order terms, which were neglected in previous analysis, we show…
Black hole solutions in general relativity come with pathologies such as singularity and mass inflation instability, which are believed to be cured by a yet-to-be-found quantum theory of gravity. Without such consistent description, one may model theory-agnostic phenomenological black holes that bypass the aforesaid issues. These so-called regular black holes are extensively studied in the literature using parameterized modifications over the black hole solutions of general relativity. However, since there exist several ways to model such black holes, it is important to study the consistency a…
In this work we investigate validity of the weak form of the cosmic censorship conjecture in the interaction of Kerr-Sen black holes with neutral test fields. Previous studies of the Klein-Gordon equation on Kerr-Sen background imply that superradiance occurs for scalar fields. We show that scalar fields can overspin a nearly extremal black hole into a naked singularity, but the modes that could overspin an extremal black hole are not absorbed due to superradiance. From Kerr analogy one can naively expect superradiance to be absent for fermionic fields. In such a case overspinning becomes gene…
We present a plausible counterexample to the weak cosmic censorship conjecture in the four-dimensional Einstein-Scalar theory with asymptotically flat boundary conditions. Our setup stems from the analysis of the massive Klein-Gordon equation on a fixed Kerr black hole background. In particular, we construct the quasinormal spectrum numerically, and analytically in the WKB approximation, then go on to compute its backreaction on the Kerr geometry. In the regime of parameters where the analytic and numerical techniques overlap we find perfect agreement. We give strong evidence for the existence…
A well posed theory of nature is expected to determine the future of an observer uniquely from a given set of appropriate initial data. In the context of general relativity, this is ensured by Penrose's strong cosmic censorship conjecture. But in recent years, several examples are found which suggest breakdown of the deterministic nature of the theory in Reissner-Nordstrom-de Sitter black holes under the influence of different fundamental fields. Nevertheless, the situation has been reassuring for the case of astrophysically meaningful Kerr-de Sitter black hole solutions which seems to respect…
Numerical evidence suggests that the superradiant instability of Kerr-AdS black holes and "black resonators" evolves to smaller and smaller scales towards a "limiting" black resonator. Using $AdS_4$ supergravity, we argue that this putative endpoint to the superradiant instability does not exist.
In this work we present an analytical proof of cosmic censorship in a Kerr-like phantom wormhole (WH) which contains a singularity that is not protected by an event horizon. We show that the naked singularity of this space-time is causally disconnected from the universe. To do so, we consider a slowly rotating limit and by means of the Hamilton-Jacobi theory separate the Hamiltonian of the geodesics into two polynomials. During this process we find a fourth conserved quantity. After examining the properties of these polynomials we conclude that the ring singularity is untouchable by any observ…
We evaluate the validity of the weak form of the cosmic censorship conjecture and the third law of black hole dynamics for Kerr-MOG black holes interacting with scalar test fields. Ignoring backreaction effects, we first show that both extremal and nearly extremal Kerr-MOG black holes can be overspun into naked singularities by scalar test fields with a frequency slightly above the superradiance limit. In addition, nearly extremal Kerr-Mog black holes can be continuously driven to extremality by test fields. Next, we employ backreaction effects based on the argument that the angular velocity o…
We study the strong gravitational lensing due to the Kerr black holes with angular momentum $a$ and the Kerr-Newman black holes with additional charge $Q$. We first derive the analytical expressions of the deflection angles of light rays that particularly diverge as they travel near the photon sphere. In this strong deflection limit, the light rays can circle around the black hole multiple times before reaching the observer, giving relativistic images. The obtained analytical expressions are then applied to compute the angular positions and the magnifications of relativistic images due to the …
We study the scenario in which a massive particle is thrown into a rapidly rotating Kerr black hole in an attempt to spin it up beyond its extremal limit, challenging weak cosmic censorship. We work in black-hole perturbation theory, and focus on non-spinning, uncharged particles sent in on equatorial orbits. We first identify the complete parameter-space region in which overspinning occurs when back-reaction effects from the particle's self-gravity are ignored. We find, in particular, that overspinning can be achieved only with particles sent in from infinity. Gravitational self-force effects…
We analyze the properties of a Kerr-like wormhole supported by phantom matter, which is an exact solution of the Einstein-phantom field equations. It is shown that the solution has a naked ring singularity which is unreachable to null geodesics falling freely from the outside. Similarly to Roger Penrose's cosmic censorship, that states that all naked singularities in the Universe must be protected by event horizons, here we conjecture from our results that a naked singularity can also be fully protected by the intrinsic properties of a wormhole's throat.
It has been argued that, starting with a slightly sub-extremal Kerr black hole instead of an extremal one, it is possible to overspin a black hole past the extremal limit and turn it into a naked singularity by sending test bodies, if one neglects radiative and self-force effects. In this work we show that (i) an extremal Kerr black hole can not be overspun as a result of the interaction with massless integer spin test fields (scalar, electromagnetic, or gravitational), (ii) overspinning can be achieved if we start with a nearly extremal black hole instead, and (iii) for the scalar field, the …
We present new results on the dynamics and gravitational-wave emission from the collapse of differentially rotating neutron stars. We have considered a number of polytropic stellar models having different values of the dimensionless angular momentum J/M^2, where J and M are the asymptotic angular momentum and mass of the star, respectively. For neutron stars with J/M^2<1, i.e., "sub-Kerr" models, we were able to find models that are dynamically unstable and that collapse promptly to a rotating black hole. Both the dynamics of the collapse and the consequent emission of gravitational waves rese…
It has been established that Christodoulou's formulation of Strong Cosmic Censorship (SCC) is violated by Reissner-Nordström-de Sitter black holes, but holds in four-dimensional Kerr-de Sitter black holes. We show that SCC is also respected by equal angular momenta (cohomogeneity-1) Myers-Perry-de Sitter (MP-dS) in odd $d \ge 5$ spacetime dimensions. This suggests that the preservation of SCC in rotating backgrounds might be a universal property of Einstein gravity and not limited to the d = 4 Kerr-dS background. As required to discuss SCC in de Sitter spacetimes, we also study important aspec…
We prove that (possibly charged) test fields satisfying the null energy condition at the event horizon cannot overspin/overcharge extremal Kerr-Newman or Kerr-Newman-anti de Sitter black holes, that is, the weak cosmic censorship conjecture cannot be violated in the test field approximation. The argument relies on black hole thermodynamics (without assuming cosmic censorship), and does not depend on the precise nature of the fields. We also discuss generalizations of this result to other extremal black holes.
The ``cosmic censorship conjecture'' asserts that all singularities arising from gravitational collapse are hidden within black holes. We investigate this conjecture in a setup of interest for tests of General Relativity: black hole solutions which are parametrically small deviations away from the Kerr solution. These solutions have an upper bound on rotation, beyond which a naked singularity is visible to outside observers. We study whether these (generic) spacetimes can be spun-up past extremality with point particles or accretion disks. Our results show that cosmic censorship is preserved f…
Recent work indicates that the strong cosmic censorship hypothesis is violated by nearly extremal Reissner-Nordstrom-de Sitter black holes. It was argued that perturbations of such a black hole decay sufficiently rapidly that the perturbed spacetime can be extended across the Cauchy horizon as a weak solution of the equations of motion. In this paper we consider the case of Kerr-de Sitter black holes. We find that, for any non-extremal value of the black hole parameters, there are quasinormal modes which decay sufficiently slowly to ensure that strong cosmic censorship is respected. Our analys…
In the conventional approach, fermionic test fields lead to a generic overspinning of black holes resulting in the formation of naked singularities. The absorption of the fermionic test fields with arbitrarily low frequencies is allowed for which the contribution to the angular momentum parameter of the space-time diverges. Recently we have suggested a more subtle treatment of the problem considering the fact that only the fraction of the test fields that is absorbed by the black hole contributes to the space-time parameters. Here, we re-consider the interaction of massless spin $(1/2)$ fields…
Recently it has been shown that quantum fields can be regular on the inner, Cauchy horizon of a rotating BTZ black hole, which appears to indicate a failure of strong cosmic censorship. We argue that, instead, what these results imply is that the inner horizon remains non-singular when leading-order backreaction of the quantum fields is computed, but, after next-order backreaction is accounted for, it will become singular. Then, strong cosmic censorship will be enforced in the BTZ black hole. We support our claims using a four-dimensional holographic dual of the system, which connects the inst…
If radiative and self-force effects are neglected, we find that feeding a test particle into a near-extremal Kerr-Newman-AdS black hole could lead to destroy their event horizon, giving rise to naked singularities. Hence radiative and self-force effects must be taken into account to further test cosmic censorship. Moreover, the allowed parameter range for this test particle is very narrow, this leaves the possibility of radiative and self-force effects considerations to cure the problem of WCC violation in Kerr-Newman-AdS spacetime.
We have developed a methodology to test the age-old cosmic censorship hypothesis in Kerr geometry. We have shown that the Kerr black hole can be overspun by particles captured from the innermost stable circular orbit. However, it appears that this does not happen for particles coming from infinity. We have also observed that overspinning becomes possible only when the black hole approaches a near-extremal limit, which approaches as we increase the black hole's mass. Our study demonstrates that an extremal black hole cannot be overspun. However, our methodology neglects backreaction and self-fo…
Rotating and/or charged black hole spacetimes possess a Cauchy horizon, beyond which Einstein's equations of General Relativity cease to be deterministic. This led to the formulation of the Strong Cosmic Censorship conjecture that such horizons become irregular under field perturbations. We consider linear field perturbations of rotating and electrically-charged (Kerr-Newman-de Sitter) black holes in a universe with a positive cosmological constant. By calculating the quasinormal modes for scalar and fermion fields, we provide evidence for the existence of weak solutions to Einstein's equation…
The new version of the gedanken experiments proposed by Sorce and Wald are designed to test the validity of the weak cosmic censorship conjecture (WCCC) by overspinning or overcharging the Kerr-Newman black hole in Einstein-Maxwell gravity. Following their setup, in this paper, we investigate the WCCC in the higher-dimensional charged black hole with a nonlinear electrodynamics source. We derive the first and seconder order perturbation inequalities of the charged collision matter based on the Iyer-Wald formalism as well as the null energy conditions, and show that they share the similar form …
