Narrow Results

In this paper, we calculate the deflection angle in the non-plasma medium by expanding the Keeton–Petters approach. We use analysis to determine how non-magnetic plasma affects the shadow of a Schwarzschild–Rindler black hole. We only consider the spherically symmetric case in which the shadow is circular. It is assumed that the plasma is independent of pressure and magnetization. From a specified spherically symmetric spacetime, we compute the results for a spherically symmetric plasma density. Our main purpose is to derive analytically a formula for the orbital radius of the shadow. Due to the diffusive nature of plasma, the shadow’s radius is influenced by the frequency of the photons. The impacts of the non-magnetic plasma are important in radio establishment. We determine that the non-magnetic plasma incorporates a decreasing impact on the shadow size for a distant observer from the Schwarzschild–Rindler black hole. Moreover, we graphically analyze the impacts of different parameters on the shadow of the corresponding black hole.

The classical cellular automata model has been modified by introducing "shadow" states or perturbations to represent the application of external signals to a configuration of discrete individual units. Simple update rules are studied to determine which of them are best suited to produce the emergent computation which can simulate signal transmission within a system. The study is made with a view to understanding electrical signalling in plant cells which are known to determine plant responses to the environment.

In this paper, we study the quantum-corrected Schwarzschild AdS black hole surrounded by quintessence matter in two folds: its thermal quantities and shadows. For this purpose, first, we present a detailed analysis of the influences of the quintessence matter field on Hawking temperature, mass, Gibbs free energy, and specific heat functions. Then, we examine the shadows by following Carter’s approach. We find that the shadow radius value takes smaller values for greater quintessence state parameter values. On the other hand, we see that the shadow radius takes greater values for greater values of the normalization parameter. Finally, in a brief section, we discuss the energy emission rate and show that the Gaussian-type plots’ peak values are also affected by the quintessence matter field parameters.

In this paper, we propose an efficient secret sharing scheme without pixel expansion. The scheme first uses the VQ-compression method to compress a secret image. This allows senders to share a larger secret image than other methods. Moreover, the proposed method also allows participants to reconstruct a lossless secret image. The generated shadows are meaningful with high quality, so the image does not attract any suspicion from attackers. Because the scheme uses XOR operation during the construction and revealing phases, it is suitable for secret sharing applications.

This paper presents an object-oriented shadow generation algorithm for a large number of convex polyhedra (objects) in a 3-D scene. In the past, the shadow volume binary space partitioning (SVBSP) tree algorithm is known to be efficient in a static environment in which the point light source can be changed. However, if a scene consists of many objects and each object consists of many polygons, the time complexity for generating and traversing an SVBSP tree increases rapidly because the SVBSP tree algorithm only deals with polygons which are components of objects. Furthermore, the SVBSP tree algorithm suffers from polygon-splitting problems resulting in a high cost as the number of polygons increases. Our approach is object-oriented in the sense that an object is used as the basic logical unit instead of polygons. In the preprocessing stage the object ordering for shadow generation is determined for all possible light source positions. At the run time, the shadow detection algorithm is executed, and if necessary, shadow fragments are generated. We also present an approach to retrieving, updating, and displaying a 3-D static or dynamic world which consists of a large number of objects.

We define and study branched shadows of 4-manifolds as a combination of branched spines of 3-manifolds and of Turaev's shadows. We use these objects to combinatorially represent 4-manifolds equipped with Spin^c-structures and homotopy classes of almost complex structures. We then use branched shadows to study complex 4-manifolds and prove that each almost complex structure on a 4-dimensional handlebody is homotopic to a complex one.

For an observer, the Black Hole (BH) shadow is the BHs 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 of shadows of Kerr BHs with scalar hair contrasting with the Kerr analogues. Additionally, an analytical solution for the Kerr shadow is derived in closed form for a ZAMO observer at an arbitrary position.

Celebrating the centennial of its first experimental test, the theory of General Relativity (GR) has successfully and consistently passed all subsequent tests with flying colors. It is expected, however, that at certain scales new physics, in particular, in the form of quantum corrections, will emerge, changing some of the predictions of GR, which is a classical theory. In this respect, black holes (BHs) are natural configurations to explore the quantum effects on strong gravitational fields. BH solutions in the low-energy effective field theory description of the heterotic string theory, which is one of the leading candidates to describe quantum gravity, have been the focus of many studies in the last three decades. The recent interest in strong gravitational lensing by BHs, in the wake of the Event Horizon Telescope (EHT) observations, suggests comparing the BH lensing in both GR and heterotic string theory, in order to assess the phenomenological differences between these models. In this work, we investigate the differences in the shadows of two charged BH solutions with rotation: one arising in the context of GR, namely the Kerr–Newman (KN) solution, and the other within the context of low-energy heterotic string theory, the Kerr–Sen (KS) solution. We show and interpret, in particular, that the stringy BH always has a larger shadow, for the same physical parameters and observation conditions.

We study the shadows of four-dimensional black holes in M-theory inspired models. We first inspect the influence of M2-branes on such optical aspects for nonrotating solutions. In particular, we show that the M2-brane number can control the circular shadow size. This geometrical behavior is distorted for rotating solutions exhibiting cardioid shapes in certain moduli space regions. Implementing a rotation parameter, we analyze the geometrical shadow deformations. Among others, we recover the circular behaviors for a large M2-brane number. Investigating the energy emission rate at high energies, we find, in a well-defined approximation, that the associated peak decreases with the M2-brane number. Moreover, we investigate a possible connection with observations (from Event Horizon Telescope or future devices) from a particular M-theory compactification by deriving certain constraints on the M$2$-brane number in the light of the $M87^{\star }$ observational parameters.

By applying the Newman–Janis Algorithm, we investigate optical behaviors of rotating Ayón–Beato–García black holes in four-dimensional Einstein Gauss–Bonnet Gravity. Exploiting the Hamilton–Jacobi mechanism, we first obtain the needed null geodesic equations of motion. We then provide analytic and numerical methods to study the associated optical aspect for certain regions of the involved moduli space. Concretely, we analyze and examine the shadow behaviors in terms of one-dimensional real closed curves. Particularly, we find various shapes including the D-ones. After that, we study graphically the corresponding astronomical observables. We compute and discuss the energy emission rate. We observe that the rotating parameter and the Gauss–Bonnet coupling have a relevant influence on the shadow geometric configurations and the energy emission rate. Moreover, we find that the nonlinear electrodynamic charge does not affect such optical behaviors. Finally, we provide a possible link with the event horizon telescope activities by imposing certain conditions on the involved black hole parameters in the $M87^{*}$ imaging aspect.

This research surveys the impact of the flavor number parameter on a four-dimensional Black Hole (BH) solution in Einstein’s nonlinear sigma model-$SU(N)$ (NLSM) in accordance with the shadow, energy emission rate, sparsity, massless scalar, and electromagnetic quasinormal mode spectra. Related investigations are being carried out to explore the influence of the flavor number parameter. In particular, the findings show that shadow behavior and energy emission rate are antinomic processes in view of the flavor number parameter. On the other hand, the $SU(N)$-NLSM BH’s quasinormal modes are computed by first calculating the effective potential generated by the perturbation of scalar and electromagnetic fields, followed by a numerical analysis based on the sixth-order WKB approach. Our results show that the QNMs of the $SU(N)$-NLSM BH damp more slowly as flavor number N increases.

Motivated by recent astrophysical observations, we investigate the shadow behaviors of four-dimensional charged rotating black holes with a cosmological constant. This study is made in terms of a reduced moduli space parameterized by the charge and the rotation parameters. For fixed observers, we analyse in some details the shadow behaviors and the corresponding naked singularities of Kerr–Newman and Kerr–Sen four-dimensional black holes in Anti-de Sitter backgrounds. Then, a comparative discussion is provided by computing the geometrical observables and the energy emission rate.

The M87* black hole shadow observation by the Event Horizon Telescope (EHT) has enabled us to test the modified gravity theories in the extreme-field regime and estimating the black hole parameters. Having this assertion, we investigate the Kerr-like rotating black holes in 4D Einstein-Gauss-Bonnet (EGB) gravity and deduce their shadows. Considering the inclination angle θ₀ = 17^o, we show that the EGB black hole shadows are smaller and more distorted than for the Kerr black holes. Modelling the M87* black hole as the EGB black hole, we predict the shadow angular size 35.7888μas ≤ θ_d ≤ 39.6192μas. The M87* black hole shadow angular size θ_d = 42±3μas, within the 1σ region, constrains the GB coupling parameter and the black hole spin parameter. Interestingly, the circularity deviation of the EGB black hole shadows is smaller than the bounded deduced for the M87* black hole.

The shadow of a wall cast by the Sun on a soccer field has been used to measure the change of the altitude and azimuth of the Sun along the day and through the seasons. The change of curvature parameter of the daily hyperbola shadow’s path, has been recovered in the days around the spring equinox 2021. The study of the daily paths has been possible with chalk and meter during school days, on this field, and the data have been reported on a spreadsheet. The students were impressed by this whole-year experiment, while normally at school the experimental sessions are one-hour long.