Narrow Results

In this study, we investigate the shadow of dynamic Phantom black hole (BH) and their observable implications with actual images of the BHs M87* and SgrA. Using the Hamilton–Jacobi formalism, we derive the null geodesic equations within the symmetry planes of spacetime, which facilitates the precise calculation of the radius of the BH shadow and its celestial coordinates. One can notice that the BH shadow’s radius exhibits a notable dependence on the BHs electric charge e and magnetic charge g. We observe that the magnetic charge g has a distinct effect on the shadow’s radius $R_s$ for the $\mathrm{\Lambda }<0$ BH spacetime compared to the asymptotically flat BH spacetime. For both spacetime configurations, an increase in the magnetic charge g correlates with an enlargement of the BH shadow’s radius. Furthermore, we introduce a plasma medium to assess the shadow’s sensitivity to variations in the plasma refractive index. This approach allows us to simulate the optical properties of the surrounding environment and its effect on the perceived size of the BH shadow. In addition, we examine how the magnetic charge affects the BHs energy emission rate, drawing a correlation with the shadow’s dimensions. We also compare the theoretical depiction of BH images with the actual images of M87* and SgrA*.

This paper is devoted to studying the optical and thermal geometrical properties of Hot NUT–Kerr–Newman–Kasuya-anti-de Sitter (HNKNK-AdS) black hole. This black hole is characterized by the NUT charge and a parameter Q that comprises the electric $Q_e$ and magnetic mono-pole parameter $Q_m$ (Kasuya parameter). We compute the image of the BH shadow in two types: (1) at $\tilde{r}\to \infty$, (2) at $\tilde{r}\to r_O$ by analytical approach. We also investigate the effect of NUT, spin, inclination angle, and cosmological constant on the shape of shadow. We analyze that for type 1, the shadow in increasing for higher values of NUT charge, the cosmological constant, rotation parameters, and inclination angle, while for type 2, by increasing these parameters, the circular symmetry of the image of the BH shadow variate. Moreover, we discuss well-known thermal geometries such as Weinhold, Ruppeiner, HPEM and Quevedo case I and II spacetime. It is found that Ruppeiner, HPEM and Quevedo (II) formulations provide physical information about the microscopic structure as compared to Weinhold and Quevedo (I) geometries. Our findings provide distinctive characteristics in the shadow and thermal geometries of this BH as compared to other black holes types.

Black hole shadows and photon spheres offer valuable tools for investigating black hole properties. Recent observations by the Event Horizon Telescope Collaboration have confirmed the existence of rotating black holes. Black hole parameters influence the observed shadow size. This paper aims to extend the work in [V. Vertogradov and A. Övgün, Analyzing the influence of geometrical deformation on photon sphere and shadow radius: A new analytical approach — spherically symmetric spacetimes, Phys. Dark Univ.45 (2024) 101541] and explores the impact of geometrical deformations on black hole shadow size using gravitational decoupling to an axially symmetric spacetime. We find that the results are more complex than the spherically symmetric case. We compare shadows in the well-known models with those of a Kerr black hole. Our approach suggests that the influence of an accretion disc on the observed shadow shape can be accurately described despite negligible impact on the black hole geometry itself.

We prove that the images of irreducible germs of plane curves by a germ of analytic morphism φ have a certain contact either with branches of the discriminant of φ or with certain infinitesimal structures (shadows) that arise from the branches of the Jacobian of φ that are mapped to a point (and therefore give rise to no branch of the discriminant).

In this paper, we calculate the weak deflection angle by Casimir wormhole and its shadow. To do so, we derive the Gaussian optical curvature and use the Gauss–Bonnet theorem (GBT). Then we find the deflection angle by Casimir wormhole in weak field limits. Moreover, we obtain the weak deflection angle in the presence of plasma medium and see the effect of the plasma medium on the weak deflection angle. Moreover, we study a shadow of Casimir wormhole and we plot and discuss them. We show the shadow of Casimir wormhole’s behavior when changing the value of a.

In this paper, we discussed optical properties of the nonlinear magnetic charged black hole surrounded by quintessence with a nonzero cosmological constant $\mathrm{\Lambda }$. Setting the state parameter $\omega =-3/2$, we studied the horizons, the photon region and the shadow of this black hole. It turned out that for a fixed quintessential parameter $\gamma$, in a certain range, with the increase of the rotation parameter $a$ and magnetic charge $Q$, the inner horizon radius increases while the outer horizon radius decreases. The cosmological horizon $r_{\mathrm{\Lambda }}$ decreases when $\gamma$ or $\mathrm{\Lambda }$ increases and it increases slightly when $a$ and $Q$ increase. The shapes of photon region were then studied and depicted through graphical illustrations. Finally, we discussed the effects of the quintessential parameter $\gamma$ and the cosmological constant $\mathrm{\Lambda }$ on the shadow of this black hole with a fixed observer position in the domain of outer communication.

We investigate the relations between the black hole shadow and charged AdS black hole critical behavior in the extended phase space. Using the thermo-shadow formalism built in Ref. 1, we reveal that the shadow radius can be considered as an efficient tool to study thermodynamical black hole systems. Based on such arguments, we build a thermal profile by varying the RN–AdS black hole temperature on the shadow silhouette. Among others, the Van der Waals-like phase transition takes place. This could open a new window on the thermal picture of black holes and the corresponding thermodynamics from the observational point of view.

A Gauss code for a virtual knot diagram is a sequence of crossing labels, each repeated twice and assigned a + or - symbol to identify over and undercrossings. Eliminate these symbols and what remains is a Gauss code for the shadow of the diagram, one type of virtual pseudodiagram. While it is now impossible to determine which particular virtual diagram the shadow resulted from, we can consider the collection of all diagrams, called resolutions of the shadow, that would yield such a code. We compute the average virtual bridge number over all these diagrams and show that for a shadow with n classical precrossings, the average virtual bridge number is .

In an earlier paper, we have analytically determined the photon regions and the shadows of black holes of the Plebański class of metrics which are also known as the Kerr–Newman–NUT–(anti-)de Sitter metrics. These metrics are characterized by six parameters: Mass, spin, electric and magnetic charges, gravitomagnetic NUT charge and the cosmological constant. Here, we extend this analysis to the Plebański–Demiański class of metrics which contains, in addition to these six parameters, the so-called acceleration parameter. All these metrics are axially symmetric and stationary type D solutions to the Einstein–Maxwell equations with a cosmological constant. We derive analytical formulas for the photon regions (i.e. for the regions that contain spherical lightlike geodesics) and for the boundary curve of the shadow as it is seen by an observer at Boyer–Lindquist coordinates (r_O, ϑ_O) in the domain of outer communication. Whereas all relevant formulas are derived for the whole Plebański–Demiański class, we concentrate on the accelerated Kerr metric (i.e. only mass, spin and acceleration parameter are different from zero) when discussing the influence of the acceleration parameter on the photon region and on the shadow in terms of pictures. The accelerated Kerr metric is also known as the rotating C-metric. We discuss how our analytical formulas can be used for calculating the horizontal and vertical angular diameters of the shadow and we estimate these values for the black holes at the center of our Galaxy and at the center of M87.

The Event Horizon Telescope’s image of the M87 black hole provides an exciting opportunity to study black hole physics. Since a black hole’s event horizon absorbs all electromagnetic waves, it is difficult to actively probe the horizon’s existence. However, with the help of a family of extremely compact, horizon-less objects, named “gravastars”, whose external spacetimes are nearly identical to those of black holes, one can test the absence of event horizons: absences of additional features that arise due to the existence of the gravastar, or its surface, can be used as quantitative evidence for black holes. We apply Gralla et al. approach of studying black hole images to study the images of two types of gravastars: transparent ones and reflective ones. In both cases, the transmission of rays through gravastars, or their reflections on their surfaces, leads to more rings in their images. For simple emission models, where the redshifted emissivity of the disk is peaked at a particular radius $r_{\mathrm{\text{peak}}}$, the position of a series of rings can be related in a simple manner to light ray propagation: a ring shows up around impact parameter $b$ whenever rays incident from infinity at $b$ intersects the disk at $r_{\mathrm{\text{peak}}}$. We show that additional rings will appear in the images of transparent and reflective gravastars. In particular, one of the additional rings for the reflective gravastar is due to the prompt reflection of light on the gravastar surface, and appears to be well separated from the others. This can be an intuitive feature, which may be reliably used to constrain the reflectivity of the black hole’s horizon.

The latest findings of static and spherically symmetric black hole solution give a potential platform to investigate the novel four-dimensional Einstein Gauss–Bonnet gravity. In order to obtain a rotating black hole solution, we first adopt the Newman Janis algorithm and study the structure of its horizons. To analyze the said black hole shadow, we move forward to compute expressions of the celestial coordinates using the geodesic equations. Furthermore, we provide a detailed analysis of the shadow size and its distortion parameter, adopting the Hioki and Maeda method, together with the applications of a supermassive black hole shadow in the center of nearby galaxy Messier 87 and obtained constraints on the relationships of spin and charge. From the obtained results, we demonstrate that both spin and coupling parameters of the black hole have a substantial influence on shadow structure. The increment in the values of these parameters diminishes the shadow radius. We also study the energy emission rate using the Hawking temperature. Furthermore, it is shown that whenever the collision of two electrically neutral test particles takes place in the vicinity of the black hole horizon, the Gauss–Bonnet black hole may serve as a particle accelerator with an infinitely large center of mass energy.

In this paper, we compute the shadow cast by a charged Morris–Thorne wormhole when the light source is a star located beyond the mouth which is opposite to the observer. First, we provide an extensive analysis of the geodesic properties of the spacetime, both for null and massive particles. The geometrical properties of this solution are such that independently of the viewing angle, some light rays always reach the observer. Additionally, the structure of the images is preserved among the different values of the charge and scales proportionally to the charge value.

Clear images are crucial for the optimal performance of various high-level vision-based tasks. However, some inevitable causes, such as bad weather and underwater conditions degrade scene visibility. The tiny particles present in the air absorb and scatter light, causing severe attenuation that results in unclear, low-brightness, and poor-contrast images. Several techniques have been introduced to restore the degradation. However, no model exists to date that can restore multiple degradations using a single model. Therefore, to improve the scene visibility, a unified model called a Multidomain Contextual Conditional Generative Adversarial Network (MCCGAN) is designed, which uses the same parameters across the domains to restore multiple degradations such as fog, haze, rain streaks, snowflakes, smoke, shadows, underwater, and muddy underwater. The proposed model has a novel addition of multiple $1\times 1$ convolutional context encoding bottleneck layers between a simple lightweight eight-block encoder and decoder with skip connections which learns the context of each input domain thoroughly, thus generating better-restored images. The MCCGAN is qualitatively and quantitatively compared to various state-of-the-art image-to-image translation models and tested on a few real unseen image domains such as smog, dust, and lightning, and the obtained results successfully improved scene visibility, proving the generalizability of MCCGAN. Moreover, the MS-COCO 2017 validation dataset is used for comparing the performance of object detection, instance segmentation, and image captioning on (1) weather-degraded images, (2) restored images by MCCGAN, and (3) ground truth images, and the results demonstrated the success of our model. An ablation study is also carried out to check the significance of the discriminator, skip connections, and bottleneck layers in MCCGAN, and the analysis suggests that MCCGAN performs better by adding a discriminator, skip connections, and four bottleneck layers in the generator architecture.

By applying the Keeton and Petters technique, we find the deflection angle as a series expansion with a specific factor of mass. We investigate the shadow structure of a regular black hole with cosmic string with a non-magnetized, pressure-free plasma around it. In order to separate the Hamilton equation and locate the photon areas, certain plasma distributions are taken into consideration. Moreover, by utilizing a new ray-tracing technique, we analyze the photon’s path around a regular black hole with cosmic string in the presence of plasma whose density depends on the radius coordinate. We also analyze the plasma effects on the shadow of black hole. We obtain an analytical formula that describes the boundary curve of the shadow for such a black hole in an expanding universe for an observer at any finite location outside the horizon. In the presence and absence of plasma, we detect deviations that are further investigated by analyzing the geometry of shadow angle at a particular value of plasma frequency.

In this study, we investigate the deflection angle of a torus-like regular charged black hole in the limit approximation of a weak field to check the effects of non-magnetic plasma and non-plasma medium. Using spacetime optical geometry, we first compute the Gaussian optical curvature. We study the light deflection angle from a charged torus-like black hole using the Gibbons and Werner approach. By taking into account the well-known Keeton–Petters approach, we validate our results. Moreover, we examine the shadow of a charged torus-like black hole by using the ray-tracing algorithm under the influence of pressureless and non-magnetized plasma and study the graphical effects of cosmological constant and charge for both anti-de Sitter and de Sitter cases on the shadow of a black hole.

We propose a new measurement method for a degree of roughness of a given object surface. This method is not to measure the degree of roughness of the object surface directly, but to estimate the roughness from surface images. Named as circulating light sources (CLS), its multiple light sources aligned in a circle illuminate sequentially, and produce images including shadow of the object surface. As the shadows on the images reflect a shape of the object surface, the shapes of the surface, concavo-convex shape, can be estimated by these shadows. In this paper, features of surface roughness are extracted by a Wavelet Multiresolution Analysis (MRA) from the shadow images produced by the CLS, and are classified by a Self-Organizing Map (SOM). A roughness of an unknown surface can be estimated by the SOM after learning.

In this paper, we construct odd unimodular lattices in dimensions n = 36,37 having minimum norm 3 and 4s = n - 16, where s is the minimum norm of the shadow. We also construct odd unimodular lattices in dimensions n = 41,43,44 having minimum norm 4 and 4s = n - 24.

For any nontrivial abelian group $A$ under addition a graph $G$ is said to be $A$-magic if there exists a labeling $f:E(G)\to A-\{0\}$ such that the vertex labeling $f^{+}$ defined as $f^{+}(v)=\sum f(uv)$ taken over all edges $uv$ incident at $v$ is a constant. An $A$-magic graph $G$ is said to be $Z_k$-magic graph if the group $A$ is $Z_k$ the group of integers modulo $k$. These $Z_k$-magic graphs are referred to as $k$-magic graphs. In this paper, we prove that the graphs such as subdivision of ladder, triangular ladder, shadow, total, flower, generalized prism, $m{\mathrm{\Delta }}_n$-snake, lotus inside a circle, square, gear, closed helm and antiprism are $Z_k$-magic graphs. Also we prove that if $G_i(1\le i\le t)$ be $Z_k$-magic graphs with magic constant zero then $G^t$ is also $Z_k$-magic.

We give a method for constructing a shadowed polyhedron from a divide. The 4-manifold reconstructed from a shadowed polyhedron admits the structure of a Lefschetz fibration if it satisfies a certain property, which is formulated as an LF-structure on a shadowed polyhedron. We will show that the shadowed polyhedron constructed from a divide satisfies this property and the Lefschetz fibration of this polyhedron is isomorphic to the Lefschetz fibration of the divide. Furthermore, applying the same technique to certain free divides we will show that the links of those free divides are fibered with positive monodromy.

We study shadows cast, under some circumstances, by a certain class of rotating wormholes and explore the dependence of the shadows on the wormhole spin. We compare our results with that of a Kerr black hole. For small spin, the shapes of the shadows cast by a wormhole and a black hole are nearly identical to each other. However, with increasing values of the spin, the shape of a wormhole shadow start deviating considerably from that of a Kerr black hole. Detection of such considerable deviation in future observations may possibly indicate the presence of a wormhole. In other words, our results indicate that the wormholes which are considered in our work and have reasonable spin can be distinguished from a black hole, through the observation of their shadows.