Direct imaging of supermassive black holes (SMBHs) at event horizon scale resolutions, as recently done by the Event Horizon Telescope, allows for testing alternative models to SMBHs such as Kerr naked singularities (KNSs). We demonstrate that the KNS shadow can be closed, open, or vanishing, depending on the spins and observational inclination angles. We study the critical parameters where the KNS shadow opens a gap, a distinctive phenomenon that does not happen with the black hole shadow. We show that the KNS shadow can only be closed for dimensionless spin $a \lesssim 1.18$ and vanishing for $a \gtrsim 1.18$ for certain ranges of inclination angles. We further analyze the effective angular momentum of photon orbits to demonstrate the fundamental connections between light geodesics and the KNS shadow geometry. We also perform numerical general relativistic ray tracing calculations, which reproduce the analytical topological change in the KNS shadow and illustrate other observational features within the shadow due to the lack of an event horizon. By comparing with black hole shadow observations, the topological change in the shadow of KNSs can be used to test the cosmic censorship hypothesis and KNSs as alternative models to SMBHs.
Degeneracy in Accretion Disk Spectra from Naked Singularities and Kerr Black Holes: Application to the AGN MCG-06-30-15
PDPIAS, Charusat University（帕迪皮阿斯，查鲁萨特大学）；International Centre for Space and Cosmology, School of Arts and Sciences, Ahmedabad University（国际空间与宇宙学中心，艺术与科学学院，艾哈迈达巴德大学）；Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research（天文与天体物理系，塔塔基础研究所）；MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院卡弗里天体物理与空间研究所，麻省理工学院）
We compare shadows cast by Schwarzschild black holes with those produced by two classes of naked singularities that result from gravitational collapse of spherically symmetric matter. The latter models consist of an interior naked singularity spacetime restricted to radii $r\leq R_b$, matched to Schwarzschild spacetime outside the boundary radius $R_b$. While a black hole always has a photon sphere and always casts a shadow, we find that the naked singularity models have photon spheres only if a certain parameter $M_0$ that characterizes these models satisfies $M_0\geq 2/3$, or equivalently, i…
We report about the possibility for interacting Kerr sources to exist in two different states - black holes or naked singularities - both states characterized by the same masses and angular momenta. Another surprising discovery reported by us is that in spite of the absence of balance between two Kerr black holes, the latter nevertheless can repel each other, which provides a good opportunity for experimental detection of the spin-spin repulsive force through the observation of astrophysical black-hole binaries.
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…
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 sing…
We investigate here the issue of observability of high energy collisions around Kerr naked singu- larity and show that the results are in contrast with the Kerr black hole case. We had shown earlier that it would be possible to have ultrahigh energy collisions between the particles close to the loca- tion r = M around the Kerr naked singularity if the Kerr spin parameter transcends the unity by an infinitesimally small amount a $\rightarrow 1^+$. The collision is between initially ingoing particle that turns back as an outgoing particle due to angular momentum barrier, with another ingoing par…
We present a detailed analysis of the orbital circular motion of electrically neutral test particles on the equatorial plane of the Kerr-Newman spacetime. Many details of the motion in the cases of black hole and naked singularity sources are pointed out. We identify four different types of orbital regions, which depend on the properties of the orbital angular momentum, and define four different kinds of naked singularities, according to the values of the charge-to-mass ratio of the source. It is shown that the presence of a particular type of counter-rotating test particles is sufficient to u…
It has recently been proposed that the accreting collapsed object GRO J1655--40 could contain a non-zero gravitomagnetic monopole, and hence could be better described with the more general Kerr-Taub-NUT (KTN) spacetime, instead of the Kerr spacetime. This makes the KTN spacetime astrophysically relevant. In this paper, we study properties of various circular orbits in the KTN spacetime, and find the locations of circular photon orbits (CPOs) and innermost-stable-circular-orbits (ISCOs). Such orbits are important to interpret the observed X-ray spectral and timing properties of accreting collap…
We study a Kerr-like black hole and naked singularity in perfect fluid dark matter (PFDM). The critical value of spin parameter $a_c$ is presented to differentiate the black hole from naked singularity. It is seen that for any fixed value of dark matter parameter $α$ the rotating object is black hole if $a\leq a_c$ and naked singularity if $a>a_c$. Also for $-2\leqα<2/3$ the size of the black hole horizons decrease whereas for $2/3<α$ it increases. We also study spin precession frequency of a test gyroscope attached to stationary observer to differentiate a black hole from naked singularity in…
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 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 investigate here the particle acceleration by Kerr naked singularities. We consider a collision between particles dropped in from infinity at rest, which follow geodesic motion in the equatorial plane, with their angular momenta in an appropriate finite range of values. When an event horizon is absent, an initially infalling particle turns back as an outgoing particle, when it has the angular momentum in an appropriate range of values, which then collides with infalling particles. When the collision takes place close to what would have been the event horizon in the extremal case, the center…
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 fre…
We study the shadow of the Cardoso-Pani-Rico (CPR) black hole for different values of the black hole spin $a_*$, the deformation parameters $ε_3^t$ and $ε_3^r$, and the viewing angle $i$. We find that the main impact of the deformation parameter $ε_3^t$ is the change of the size of the shadow, while the deformation parameter $ε_3^r$ affects the shape of its boundary. In general, it is impossible to test the Kerr metric, because the shadow of a Kerr black hole can be reproduced quite well by a black hole with non-vanishing $ε_3^t$ or $ε_3^r$. Deviations from the Kerr geometry could be constrain…
We investigate the gravitational lensing by spinning Proca stars and the shadows and lensing by Kerr black holes (BHs) with synchronised Proca hair, discussing both theoretical aspects and observational constraints from the Event Horizon Telescope (EHT) M87* and Sgr A* data. On the theoretical side, this family of BHs interpolates between Kerr-like solutions -- exhibiting a similar optical appearance to that of Kerr BHs -- to very non-Kerr like solutions, exhibiting exotic features such as cuspy shadows, egg-like shadows and ghost shadows. We interpret these features in terms of the structure …
A black hole casts a shadow as an optical appearance because of its strong gravitational field. We study how to determine the spin parameter and the inclination angle by observing the apparent shape of the shadow, which is distorted mainly by those two parameters. Defining some observables characterizing the apparent shape (its radius and distortion parameter), we find that the spin parameter and inclination angle of a Kerr black hole can be determined by the observation. This technique is also extended to the case of a Kerr naked singularity.
The Event Horizon Telescope (EHT) is taking the first images of black holes resolved at horizon scales to measure their shadows and probe accretion physics. A promising avenue for testing the hypothesis that astrophysical black holes are described by the Kerr solution to Einstein's equations is to compare the size and shape of the shadow a black hole casts on the surrounding emission to the predictions of the Kerr metric. We develop here an efficient parametric framework to perform this test. We carry out ray-tracing simulations for several parametrized non-Kerr metrics to create a large data …
We give a new theoretical basis for examination of the presence of the Kerr black hole (KBH) or the Kerr naked singularity (KNS) in the central engine of different astrophysical objects around which astrophysical jets are typically formed: X-ray binary systems, gamma ray bursts (GRBs), active galactic nuclei (AGN), etc. Our method is based on the study of the exact solutions of the Teukolsky master equation for electromagnetic perturbations of the Kerr metric. By imposing original boundary conditions on the solutions so that they describe a collimated electromagnetic outflow, we obtain the spe…
Geodesics and Shadows in the Kerr-Bertotti-Robinson Black Hole Spacetime
Beijing Normal University（北京师范大学）；Key Laboratory of Multiscale Spin Physics (Ministry of Education), Beijing Normal University（北京师范大学多尺度自旋物理教育部重点实验室）；Tsung-Dao Lee Institute, Shanghai Jiao-Tong University（上海交通大学汤川研究所）；Institute of Fundamental Physics and Quantum Technology, & School of Physical Science and Technology, Ningbo University（宁波大学基础物理与量子技术学院、物理科学与技术学院）；School of Physics, Peking University, & Center for High Energy Physics（北京大学物理学院、高能物理中心）
We analyze the properties of circular orbits of test particles on the equatorial plane of a rotating central mass whose gravitational field is described by the Kerr spacetime. For rotating black holes and naked singularities we explore all the spatial regions where circular orbits can exist and analyze the behavior of the energy and the angular momentum of the corresponding test particles. In particular, we find all the radii at which a test particle can have zero angular momentum due to the repulsive gravity effects generated by naked singularities. We classify all the stability zones of circ…
Phase Transitions, Shadows, and Microstructure of Kerr-anti-de Sitter Black Holes from Geometrothermodynamics
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Dipartimento di Fisica and Icra, Università di Roma “La Sapienza”（罗马第一大学物理系及ICRA）；Al-Farabi Kazakh National University（阿尔法拉比哈萨克国立大学）
For an observer, the Black Hole (BH) shadow is the BH's apparent image in the sky due to the gravitational lensing of nearby radiation, emitted by an external source. A recent class of solutions dubbed Kerr BHs with scalar hair possess smaller shadows than the corresponding Kerr BHs and, under some conditions, novel exotic shadow shapes can arise. Thus, these hairy BHs could potentially provide new shadow templates for future experiments such as the Event Horizon Telescope. In order to obtain the shadows, the backward ray-tracing algorithm is briefly introduced, followed by numerical examples …
In this work, we study the shadow of Kerr black hole surrounded by an axisymmetric plasma, whose density takes a Gaussian distribution in the polar direction. Along the radial direction, we consider two models: in model A the density of the plasma decays in a power law; in model B the density obeys a logarithmic Gaussian distribution. Using the numerical backward ray-tracing method, we find that the size of the shadow is sensitive to the inclination angle of the observer due to the polar distribution of the density of the plasma. In particular, we pay special attention to the model B and inves…
In a previous paper, one of us has showed that, at least in some cases, the Kerr-nature of astrophysical black hole candidates is extremely difficult to test and current techniques, even in presence of excellent data not available today, cannot distinguish a Kerr black hole from a Bardeen one, despite the substantial difference of the two backgrounds. In this paper, we investigate if the detection of the "shadow" of nearby super-massive black hole candidates by near future mm/sub-mm very long baseline interferometry experiments can do the job. More specifically, we consider the measurement of …
The unprecedented image of the M87* supermassive black hole has sparked some controversy over its usefulness as a test of the general relativistic Kerr metric. The criticism is mainly related to the black hole's quasi-circular shadow and advocates that its radius depends not only on the black hole's true spacetime properties but also on the poorly known physics of the illuminating accretion flow. In this paper we take a sober view of the problem and argue that our ability to probe gravity with a black hole shadow is only partially impaired by the matter degrees of freedom and the number of non…
Motivated by the lack of rotating solutions sourced by matter in General Relativity as well as in modified gravity theories, we extend a recently discovered exact rotating solution of the minimal Einstein-scalar theory to its counterpart in Eddington-inspired Born-Infeld gravity coupled to a Born-Infeld scalar field. This is accomplished with the implementation of a well-developed mapping between solutions of Ricci-Based Palatini theories of gravity and General Relativity. The new solution is parametrized by the scalar charge and the Born-Infeld coupling constant apart from the mass and spin o…
The black hole shadow, first observed by the Event Horizon Telescope in 2017, is the newest method for studying black holes and understanding gravity. Much work has gone into understanding the shadow of a Kerr black hole, including all of the complex astrophysics of the accretion disk, and there are numerous studies of the ideal shadow in non-Kerr black holes and exotic compact objects. This paper presents one of the first studies of the black hole shadow of non-Kerr black holes when the illumination source is an accretion disk. In particular, the ability of current and future very long baseli…
Within 5-10 years, very-long baseline interferometry (VLBI) facilities will be able to directly image the accretion flow around SgrA$^*$, the super-massive black hole candidate at the center of the Galaxy, and observe the black hole "shadow". In 4-dimensional general relativity, the no-hair theorem asserts that uncharged black holes are described by the Kerr solution and are completely specified by their mass $M$ and by their spin parameter $a$. In this paper, we explore the possibility of distinguishing Kerr and Bardeen black holes from their shadow. In Hioki & Maeda (2009), under the assumpt…
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 …
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…
Capturing the image of the shadow cast by the event horizon of an illuminated black hole is, at the most basic level, an experiment of extreme light deflection in a strongly curved spacetime. As such, the properties of an imaged shadow can be used to probe the general relativistic Kerr nature of astrophysical black holes. As an example of this prospect, it is commonly asserted that a shadow can test the validity of the theory's famous `no hair theorem' for the black hole's mass and spin multipole moments. In this paper, we assess this statement by calculating the shadow's equatorial radius in …
Reshaping the inner shadow of a Kerr black hole by a torn accretion disk
School of Mathematics and Physics, University of South China（南华大学数学与计算学院）；School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）；Department of Mechanics, Chongqing Jiaotong University（重庆交通大学力学系）
Using backwards ray tracing, we study the shadows of Kerr black holes with scalar hair (KBHsSH). KBHsSH interpolate continuously between Kerr BHs and boson stars (BSs), so we start by investigating the lensing of light due to BSs. Moving from the weak to the strong gravity region, BSs - which by themselves have no shadows - are classified, according to the lensing produced, as: $(i)$ non-compact, which yield no multiple images; $(ii)$ compact, which produce an increasing number of Einstein rings and multiple images of the whole celestial sphere; $(iii)$ ultra-compact, which possess light rings…
Tilted thin accretion disks in the full Kerr spacetime and their implications
Manipal Centre for Natural Sciences, Manipal Academy of Higher Education（马尼帕尔高等教育局马尼帕尔自然科学中心）；Tata Institute of Fundamental Research（塔塔基础研究所）；MIT Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology（麻省理工学院卡弗里天体物理与空间研究所）
We investigate in detail the circular motion of test particles on 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 an…
Observations of the black hole shadow of supermassive black holes, such as Sagittarius A* at the center of our Milky Way galaxy, allow us to study the properties of black holes and the nature of strong-field gravity. According to the Kerr hypothesis, isolated, stationary, and axisymmetric astrophysical black holes are described by the Kerr metric. The Kerr hypothesis holds in General Relativity and in some modified gravity theories, but there are others in which it is violated. In principle, black hole shadow observations can be used to determine if the Kerr metric is the correct description f…
The final fate of gravitational collapse of massive stars has been a subject of interest for a long time since such a collapse may lead to black holes and naked singularities alike. Since, the formation of naked singularities is forbidden by the cosmic censorship conjecture, exploring their observational differences from black holes may be a possible avenue to search for these exotic objects. The simplest possible naked singularity spacetime emerges from the Einstein massless scalar field theory with the advantage that it smoothly translates to the Schwarzschild solution by the variation of th…
We examine the possibility for the existence of gravitomagnetic monopole ($n_*$) in M87* by using the results obtained from its first Event Horizon Telescope image. By numerically deducing the shadow sizes in Kerr-Taub-NUT (KTN) spacetime, we show that the shadow size increases with increasing $|n_*|$ for a fixed Kerr parameter $|a_*|$ in case of the KTN black hole, whereas for a KTN naked singularity it increases with increasing $n_*$ for a fixed $a_* > 0$ if $n_* > -\cot 17^{\circ}$ . In general, the asymmetry of shadow shape increases if the central dark object in M87 is a KTN/Kerr naked si…
We study the properties of the relativistic, steady, axisymmetric, low angular momentum, inviscid, advective, geometrically thin accretion flow in a Kerr-Taub-NUT (KTN) spacetime which is characterized by the Kerr parameter ($a_{\rm k}$) and NUT parameter ($n$). Depending on $a_{\rm k}$ and $n$ values, KTN spacetime represents either a black or a naked singularity. We solve the governing equations that describe the relativistic accretion flow in KTN spacetime and obtain all possible global transonic accretion solutions around KTN black hole in terms of the energy $({\cal E})$ and angular momen…
Recently double black hole vacuum and electrovacuum metrics attracted attention as exact solutions suitable for visualization of ultra-compact objects beyond the Kerr paradigm. However, many of the proposed systems are plagued with ring curvature singularities. Here we present a new simple solution of this type which is asymptotically Kerr, has zero electric and magnetic charges, but is endowed with magnetic dipole moment and electric quadrupole moment. It is manifestly free of ring singularities, and contains only a mild string-like singularity on the axis corresponding to a distributional en…
We study the effect caused by external magnetic fields on the observed thermal spectra and iron line profiles of thin accretion discs formed around Kerr black holes and naked singularities. We aim to provide a tool that can be used to estimate the presence of magnetic fields in the neighbourhood of a compact object and to probe the cosmic censorship conjecture in these particular astrophysical environments. We developed a numerical scheme able to calculate thermal spectra of magnetised Page-Thorne accretion discs formed around rotating black holes and naked singularities as seen by an arbitrar…
We study here the precession of the spin of a test gyroscope attached to a stationary observer in the Kerr spacetime, specifically, to distinguish naked singularity (NS) from black hole (BH). It was shown recently that for gyros attached to static observers, their precession frequency became arbitrarily large in the limit of approach to the ergosurface. For gyros attached to stationary observers that move with non-zero angular velocity $Ω$, this divergence at the ergosurface can be avoided. Specifically, for such gyros, the precession frequencies diverge on the event horizon of a BH, but are f…
We consider a simple model of a black hole surrounded by a toroidal structure and experiencing deformation due to magnetic field and the tidal force. For this system we construct the shadows of Preston-Poisson black hole, apply it to supermassive black hole $M87^*$ and compare it with the shadows of corresponding Schwarzschild and Kerr black holes. We find that for large deviation parameters $B$ and $E$ the shadow of Preston-Poisson black hole is clearly distinguishable from Kerr black hole provided the angular resolution of measurements is of order $μ\mathrm{arcsec}$.
We study the shadows cast by near-extremal Kerr-MOG black holes for different values of the parameter in modified gravity (MOG). In particular, we consider an isotropic emitter orbiting near such black holes and analytically compute the positions, fluxes and redshift factors of their images. The size of the shadow decreases when the modified parameter is increased. For each shadow, the images of the emitter appear on a special part of the shadow which has a rich structure. The primary image and secondary images are similar to those produced for the near-extremal (high spin) Kerr black hole, bu…
We construct a novel class of spherically symmetric and asymptotically flat black holes and naked singularities surrounded by anisotropic dark matter fluid with the equation of state (EoS) of the form $P_t=ωρ$. We assume that dark matter is made of weakly interacting particles orbiting around the supermassive black hole in the galactic center and the dark matter halo is formed by means of Einstein clusters having only tangential pressure. In the large distance from the black hole, we obtain the constant flat curve with the upper bound for the dark matter state parameter $ω\lesssim 10^{-7}$. To…
