Size Of Shadow Research Articles

Shadow of novel rotating black hole in GR coupled to nonlinear electrodynamics and constraints from EHT results

We study the optical properties of spacetime around a novel black hole in general relativity coupled to nonlinear electrodynamics, which is asymptotically flat. First, we study the angular velocity and Lyapunov exponent in unstable photon circular orbits in the novel spherically symmetric black hole spacetime. Later, we obtain the rotating black hole solution using the Newman–Janis algorithm and determine the event horizon properties of the black hole. We analyze the effective potential for the circular motion of photons in the spacetime of the novel rotating black hole. Also, we analyze the photon sphere around the novel black hole and its shadow using celestial coordinates. We obtain that an increase of the black hole spin and charge as well as nonlinear electrodynamics field nonlinearity parameters causes an increase in the distortion parameter of the black hole shadow, while, the area of the shadow and its oblateness decrease. Moreover, we also obtain the constraint values for the black hole charge and the nonlinearity parameters using Event Horizon Telescope data from shadow sizes of supermassive black holes Sgr A* and M87*. Finally, the emission rate of black hole evaporation through Hawking radiation is also studied.

Strong gravitational lensing by Bardeen black holes in 4D EGB gravity: Constraints from supermassive black holes

Observation indicates that many nearby galaxies host supermassive central black holes. We use the Bardeen black holes in four-dimensional Einstein–Gauss–Bonnet (4D EGB) gravity, with additional parameters-the coupling constant α̃ and charge q, as central black holes in various galaxies to investigate gravitational lensing properties in strong field regime. Taking the supermassive black holes Sgr A* and M87* as the lens, we compare observable signatures of 4D EGB Bardeen black holes with those of the Schwarzschild black holes. In the case of 4D EGB Bardeen black holes we observed that he angular position θ∞ for Sgr A* ∈ (23.19, 25.56) μ as, whereas for M87* it is ∈ ( 17.94,19.78) μ as. Further, the angular separation s, which is an increasing function of α̃ and q for Sgr A* and M87* differs significantly, respectively, in (0.032, 0.15) μ as and (0.025, 0.115) μ as. The deviations of the lensing observables Δθ∞ and Δs for 4D EGB Bardeen black hole (α̃=0.9,q=0.09) from the Schwarzschild black hole, respectively, can reach up to 2.38μ as and 0.12μ as for Sgr A* , 1.84μ as and 0.09μ as for M87*. On the other hand, the relative magnification ∈ (4.66,6.82). Considering twenty-one massive central black holes as lens, we also estimate the time delay ΔT2,1s between the first and second relativistic image to find that, e.g., the time delay for Sgr A* and M87*, respectively, can reach ∼9.86 min and ∼16023.93 min. We also show that the existing shadow size measurements place strong constraints on the parameters considered Bardeen model. This combination of gravitational lensing and EHT results may complement comprehensive restrictions on modifications of the general relativity.

Observational signatures of Rotating compact objects in Plasma space–time

We have investigated the characteristics of shadows cast by the Kerr black hole in the presence of plasma and compared them to those of a rotating wormhole in a uniform plasma space–time for an observer at infinity. Interestingly, for the same uniform plasma density, the apparent shadow size of the rotating wormhole is always greater than that of the Kerr black hole. To further distinguish the two compact objects we studied the deflection angle and did a comparative study in the presence of the uniform and non-uniform plasma profiles. The goal of this whole exercise is to deepen our understanding of the observational phenomena of these astrophysical objects. The analysis reveals the importance of specific plasma distribution profiles, the impact of plasma on the shadow diameter, and the behavior of deflection angles in different plasma scenarios. We have calculated constraints on the plasma parameters by considering observational data and employing analytical formulations. Our work therefore provides valuable insights into the behavior of light rays near compact objects in plasma space–time.

Rotating black holes surrounded by a dark matter halo in the galactic center of M87 and Sgr A[formula omitted]

In this paper, we construct the solutions of modified Schwarzschild spacetime with three kinds of dark matter profiles, i.e. the Beta profiles, Moore profiles and Fermionic halos profiles. In order to make the models more realistic, by using the modified Newman–Janis algorithm (MNJA), we extend our solution to obtain three rotating black holes surrounded by dark matter halo and discuss the black hole properties such as the event horizon, ergoregion, geodesics of null particles and the black hole shadow. We consider two specific examples, i.e. using the present values for the parameters of the dark matter density profiles for the Sgr A∗ black hole and M87 central black hole, it shows that the effects of the dark matter on the size of shadows are almost negligible compared to the shadow of Kerr black hole. Besides, in specific condition having dark matter with very high density, we show that the shadow images of Beta model rotating black hole increase, but the shadow images of Moore model and Fermionic model rotating black holes decrease, furthermore, the Moore profile has the largest deviation, the Beta profile has the least deviation and the deviation of Fermionic halo model is in the middle. These phenomena may provides us with a possibility: the effect of dark matter on the apparent shadow shape could shed some light on mass density profiles of dark matter halo of a galaxy, by studying black holes in dark matter, it may provide an inspiration for us to indirectly detect dark matter.

Microlensing black hole shadows

ABSTRACT A detailed analysis is presented of gravitational microlensing by intervening compact objects of the black hole shadows imaged by the Event Horizon Telescope (EHT). We show how the centre, size, and shape of the shadow depend on the Einstein angle relative to the true/unlensed shadow size, and how the location of the lens affects the shift, size, and asymmetry of the black hole shadow due to microlensing. Assuming a supermassive black hole (SMBH) casts a circular-shaped true shadow, microlensing can create an asymmetry of up to approximately 8 per cent, which is twice the asymmetry caused by the SMBH’s spin and its tilt relative to us. Furthermore, the size can be enhanced by ∼50 per cent of the true shadow. Currently, the terrestrial baselines of EHT lack the resolution to detect microlensing signatures in the shadows. However, future expansions of EHT, including space-based baselines at the Moon and L2, could potentially enable the detection of microlensing events. For Sgr A*, an event rate of 0.0014 per year makes the microlensing phenomena difficult to observe even with space-based baselines for the stellar population in the stellar bulge and stellar disc for lens masses ∼M⊙. None the less, the presence of a cluster of 20 000 stellar-mass black holes in the central parsec of the Milky Way, expected to arise from dynamical friction acting on infalling stellar clusters, significantly boosts the event rate. Hence, continuously monitoring the shadow of Sgr A* could offer novel insights into the compact object population surrounding the Galactic Centre.

Red quantum-dot common layer for organic-quantum-dot hybrid light-emitting diodes for full-color displays

Organic and quantum dot (QD) light-emitting diodes (OLEDs and QLEDs, respectively) have been known for their practical application in full-color displays. Each primary color-emitting layer (EML) needs to be patterned via fine metal shadow masks (FMMs) or inkjet printing. However, the FMM method suffers from a shadow effect, misalignment, and size limitation, while inkjet printing hinders fine patterning, which disrupts high-resolution, large-scale fabrication. Here, we show a novel organic–QD hybrid device architecture by introducing a red QD common layer (QDCL). Since the QDCL is deposited onto all sub-pixels in a solution process without patterning, one patterning step for the red sub-pixel is reduced for full-color display fabrication. The green and blue OLEDs incorporating a red-emitting QDCL emitted their own color, owing to the effective exciton confinement within the EML by adopting a buffer layer, while the QDs in the QDCL emitted saturated red light. As a result, we could demonstrate a full-color organic–QD hybrid light-emitting device fabricated on a single substrate using the QDCL. We believe our strategy would help fabricate full-color and high-resolution displays with reduced manufacturing costs and time.

A shadow study for a static dyonic black hole with a global monopole surrounded by perfect fluid

In this paper, we mainly study the shadow and observable features of a dyonic black hole (DBH) with a global monopole surrounded by perfect fluid under various profiles of accretions. We investigate the influence of model parameters on the observational signatures and space-time structure of black holes (BHs). We observe that the value of bps\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$b_{ps}$$\\end{document} increases with the increasing values of α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} and η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta $$\\end{document}, while it decreases with the increasing values of the electromagnetic parameter. We found that the corresponding regions and the observed specific intensities of the direct, lensing and photon ring emissions dramatically changed according to the variation of BH state parameters. It is noticed that the total observed flux is dominated by the direct emission and the lensing ring makes a small contribution while the photon ring makes a negligible contribution due to its exponential narrowness, even the photon ring intersects the thin plane more than three times to pick up a larger intensity. Assuming the spherically symmetric accretion disk, it is found that due to the Doppler effect of infalling motion, shadows of infalling accretion are found to be darker as compared to static ones. However, the size and position of the DBH shadows do not change in both cases, implying that the BH’s shadow size depends on the geometric space-time and the shadow’s luminosities rely on the accretion flow models. Finally, the discussion is done analytically and numerically, and ray-tracing methods are adopted to obtain the proper visualizations.

The persistent shadow of the supermassive black hole of M 87

In April 2019, the Event Horizon Telescope (EHT) Collaboration reported the first-ever event-horizon-scale images of a black hole, resolving the central compact radio source in the giant elliptical galaxy M 87. These images reveal a ring with a southerly brightness distribution and a diameter of ∼42 μas, consistent with the predicted size and shape of a shadow produced by the gravitationally lensed emission around a supermassive black hole. These results were obtained as part of the April 2017 EHT observation campaign, using a global very long baseline interferometric radio array operating at a wavelength of 1.3 mm. Here, we present results based on the second EHT observing campaign, taking place in April 2018 with an improved array, wider frequency coverage, and increased bandwidth. In particular, the additional baselines provided by the Greenland telescope improved the coverage of the array. Multiyear EHT observations provide independent snapshots of the horizon-scale emission, allowing us to confirm the persistence, size, and shape of the black hole shadow, and constrain the intrinsic structural variability of the accretion flow. We have confirmed the presence of an asymmetric ring structure, brighter in the southwest, with a median diameter of 43.3−3.1+1.5 μas. The diameter of the 2018 ring is remarkably consistent with the diameter obtained from the previous 2017 observations. On the other hand, the position angle of the brightness asymmetry in 2018 is shifted by about 30° relative to 2017. The perennial persistence of the ring and its diameter robustly support the interpretation that the ring is formed by lensed emission surrounding a Kerr black hole with a mass ∼6.5 × 109 M⊙. The significant change in the ring brightness asymmetry implies a spin axis that is more consistent with the position angle of the large-scale jet.

Observational signatures of a static f(R) black hole with thin accretion disk

In this study, we focus on a static spherically symmetric f(R) black hole spacetime characterized by a linear dark matter-related parameter. Our investigation delves into understanding the influence of different assumed values of this parameter on the observable characteristics of the black hole. To fulfill this task, we investigate the light deflection angles, which are inferred from direct analytical calculations of null geodesics. To examine the black hole’s properties further, we assume an optically thin accretion disk and explore various emission profiles. Additionally, we investigate the shadow cast by the illuminated black hole when affected by the disk. Furthermore, we simulate the brightness of an infalling spherical accretion in the context of silhouette imaging for the black hole. Our findings indicate that, except for some specific cases, the observed brightness of the accretion disk predominantly arises from direct emission, rather than lensing and photon rings. Moreover, we reveal that the linear dark parameter of the black hole significantly influences the shadow size and brightness. Our discussion covers both analytical and numerical approaches, and we utilize ray-tracing methods to produce accurate visualizations.

Shadow and weak gravitational lensing for Ellis-Bronnikov wormhole* *This work is partly Supported by Grants F-FA-2021-432, F-FA-2021-510, and MRB-2021-527 of the Ministry of Higher Education, Science and Innovations of the Republic of Uzbekistan

In this study, we investigated the gravitational weak lensing and shadow of the Ellis-Bronnikov wormhole. First, we studied the photon motion in a plasma medium and a wormhole shadow. It was shown that the radius of the photon sphere of the Ellis-Bronnikov wormhole and the size of the wormhole shadow become larger under the influence of the parameter a. The upper limit of the parameter a in the Ellis-Bronnikov wormhole spacetime was obtained. Second, we investigated the weak gravitational lensing for the Ellis-Bronnikov wormhole and calculated the deflection angle for uniform and non uniform plasma cases. The value of the deflection angle for uniform plasma increased with the increase in plasma parameter value, and vice versa for non uniform plasma. We found that, under the influence of the parameter a, the values of the deflection angles for two cases decreased. Finally, we investigated the magnification of image brightness using the deflection angle of the light rays around the wormhole in the Ellis-Bronnikov theory.

Analysis of Moon shadow from 2021-2022 LHAASO WCDA Data

The Large High Altitude Air Shower Observatory (LHAASO) is a major ground-based array of cosmic-ray (CR) detectors in the Sichuan Province in China. The Water Cherenkov Detector Array (WCDA) is an essential component of LHAASO, which is designed to measure ~1-50 TeV CRs and gamma rays. As observed on Earth, the Moon blocks some CRs to create a shadow. Although CRs are mostly protons, WCDA can probabilistically identify some constituents (mostly electrons and photons) of CRs which produce electromagnetic (EM) showers in the atmosphere, using the “compactness” (C) of the showers as the criterion for which the higher C indicates the higher probability of an event being EM. The observed CR Moon shadow positions must be shifted from that of the actual Moon due to the deflection of charged particles by the Earth’s magnetic field. We analyze the LHAASO WCDA data from March 2021 to December 2022 to study the properties of the CR Moon shadows for events with C < 10 and C > 10, such as the shifted position and the size of the shadow at different energies. We found that i) CR shadows’ shifts decrease when energy increases, and ii) the higher the energy, the size of the CR shadows are more compact. This analysis is useful for detector calibration, event selection study, and understanding CR trajectories in the geomagnetic field.

Quantum corrections on geodesic structure and shadow behavior of the Schwarzschild black hole

Point-like singularities of black hole space–times in general theory of relativity (GR) and alternative theories of gravity are one of the controversial issues for decades. One way to remove the central singularity of the Schwarzschild black hole is the Kazakov–Solodukhin (KS) proposal, which takes into account the effects of quantum field theory within the GR framework leading to the KS black hole. On the other hand, the Event Horizon Telescope (EHT) becomes a noteworthy tool for constraining the black hole parameters in gravitational theories. Hence, in this work, we plan to study the null geodesic structure, shadow behavior, energy emission rate, and deflection angle of the KS black hole. Then, we constrain the quantum correction parameter of the KS black hole via EHT data of the M87* supermassive black hole. We observe that increasing the quantum effects in the KS black hole leads to amplification of the shadow size of the KS black hole.

Investigating shadow images and rings of the charged Horndeski black hole illuminated by various thin accretions

In this paper, we investigate the shadows and rings of the charged Horndeski black hole illuminated by accretion flow that is both geometrically and optically thin. We consider two types of accretion models: spherical and thin-disk accretion flow. We find that in both types of models, the size of the charged Horndeski black hole shadow decreases with the increase of the charge, and it decreases more slowly for the Reissner–Nordström (RN) black hole. In the spherical accretion flow model, we find that the increase of the charge of Horndeski black hole brightens the light ring around it, and it brightens more significantly in comparison with RN black hole. Due to the Doppler effect, the charged Horndeski black holes with accretion flow of radial motion have darker shadows than those with the static accretion flow, but the size of the shadow is not affected by accretion flow motion. In the thin disk-shaped accretion flow model, we find that the brightness of the light ring around the charged Horndeski black hole is dominated by the direct emission from the accretion flow, and the contribution from lensed rings is relatively small, and that from the photon rings is negligible. We also find that the ring brightness decreases as the charge of Horndeski black hole increases, and the decrease is more significant than that in the RN black hole case. Moreover, the radiation position of the accretion flow can affect the shadow size and the ring brightness of the charged Horndeski black hole.

Shadow Implications: What Does Measuring the Photon Ring Imply for Gravity?

With the imaging and characterization of the horizon-scale images of M87* and Sgr A* by the Event Horizon Telescope (EHT), it has become possible to resolve the near-horizon region of astrophysical black holes. As a result, there has been considerable interest in the implications of the measurement of the shadow size, i.e., the asymptotic photon ring. We explore the general implications of such a measurement, identifying what is and, more importantly, is not constrained by such measurements, with applications to EHT and future instruments. We consider a general spherically symmetric metric, which effectively applies for a polar observer (appropriate for M87*) in the slow rotation limit. We propose a nonperturbative, nonparametric spacetime-domain characterization of shadow size and related measurements that makes explicit the nature and power (or lack thereof) of shadow-size-based constraints, and facilitates comparisons among observations and targets.

Polarized Anisotropic Synchrotron Emission and Absorption and Its Application to Black Hole Imaging

Low-collisionality plasma in a magnetic field generically develops anisotropy in its distribution function with respect to the magnetic field direction. Motivated by the application to radiation from accretion flows and jets, we explore the effect of temperature anisotropy on synchrotron emission. We derive analytically and provide numerical fits for the polarized synchrotron emission and absorption coefficients for a relativistic bi-Maxwellian plasma (we do not consider Faraday conversion/rotation). Temperature anisotropy can significantly change how the synchrotron emission and absorption coefficients depend on observing angle with respect to the magnetic field. The emitted linear polarization fraction does not depend strongly on anisotropy, while the emitted circular polarization does. We apply our results to black hole imaging of Sgr A* and M87* by ray tracing a GRMHD simulation and assuming that the plasma temperature anisotropy is set by the thresholds of kinetic-scale anisotropy-driven instabilities. We find that the azimuthal asymmetry of the 230 GHz images can change by up to a factor of 3, accentuating (T ⊥ > T ∥) or counteracting (T ⊥ < T ∥) the image asymmetry produced by Doppler beaming. This can change the physical inferences from observations relative to models with an isotropic distribution function, e.g., by allowing for larger inclination between the line of sight and spin direction in Sgr A*. The observed image diameter and the size of the black hole shadow can also vary significantly due to plasma temperature anisotropy. We describe how the anisotropy of the plasma can affect future multifrequency and photon ring observations. We also calculate kinetic anisotropy-driven instabilities (mirror, whistler, and firehose) for relativistically hot plasmas.

A compressed sensing-based progressive secret image sharing scheme and security analysis

Cryptographic secret image sharing (SIS) allows a secret image to be shared among participants, and any authorized set of participants can reconstruct the secret. In this paper, we first propose a conceptually simple way to construct a progressive SIS scheme based on semi-tensor product compressed sensing (STP-CS). In the sharing phase, the dealer employs STP-CS to compress the secret image and extracts several different rows of the compressed image in turn. Then the sub-shadows for participants are formed. In addition, he needs to employ a perfect secret sharing to share the measurement matrix (or an initial state of the linear feedback shift register) among all participants. Finally, the sub-shadow and the share of the measurement matrix together constitute the shadow of each participant. In the combination phase, any legitimate access structure can reconstruct the secret image gradually. The perfect secret sharing ensures that the combination phase can work if and only if the access structure is authorized. Simultaneously, the use of STP-CS ensures that the proposed scheme has the properties of gradual reconstruction, noise-resilience, and smaller shadow size. Also, we have proven that the proposed scheme achieves the extended Wyner-sense perfect secrecy. Besides, we provide an extend version, referred to as homomorphic secret image sharing (HSIS), for improving the efficiency of the combination algorithm. HSIS can outsource the combination phase to the cloud servers securely.

Shadows and photon rings of a spherically accreting Kehagias–Sfetsos black hole

By considering Kehagias–Sfetsos black hole in the framework of the Hořava–Lifshitz gravity, we study the optical appearance of such black holes surrounded by spherical accretion flow. For the static/ infalling spherical accretion flow, we compute the observed specific intensity as a function of impact parameter. We also investigate the effect of the Hořava parameter and accreting matter on the luminosity of shadows and photon rings. It is found that an increase in the Hořava parameter decreases the shadow size, while the shadows and photon rings luminosities increase. Moreover, we constrain the Hořava parameter from the observational data reported by the Event Horizon Telescope for M87* and Sgr A*.

4D Einstein-Gauss-Bonnet black hole in Power-Yang-Mills field: a shadow study

We consider a static black hole immersed in the Power-Yang-Mills field in four-dimensional Einstein-Gauss-Bonnet gravity and investigate the effect of various parameters on the radius of the photon sphere. The modified form of the Newman-Janis algorithm is used for obtaining a rotating black hole solution in this gravity. Further, we try to explore the influence of the Yang-Mills magnetic charge Q with power q, Gauss-Bonnet parameter α, and spin a on the horizon radius. The geodesic equations are constructed by incorporating the Hamilton-Jacobi formalism. The radial component of the geodesic equations gives the effective potential which is further used in deriving the mathematical structure for the shadows by using Bardeen's procedure for a fixed observer at infinity. The shadows are calculated and plotted in terms of two celestial coordinates for an equatorial observer. It is observed that all the parameters have a very significant effect on the shadow and related physical observables. We also obtain the constraint values for the spin, magnetic charge, and Gauss-Bonnet parameters, using the shadow size of supermassive black holes Sagittarius A* and M87* from the EHT observations for the cases of q = 0.6 and q = 0.9. It is shown that there are upper and lower bounds for the charge and spin of M87* at q = 0.6, while only the upper bounds for the charge and spin of Sagittarius A*. Finally, we investigate the energy emission rate in the Hawking radiation around the 4D Einstein-Gauss-Bonnet black hole in the Power-Yang-Mills field.

Probing the Starobinsky-Bel-Robinson gravity by photon motion around the Kerr-type black hole in non-uniform plasma

This study investigates the optical properties of a rotating black hole in Starobinsky-Bel-Robinson gravity, characterized by the additional parameter β. The black hole is assumed to be surrounded by non-uniform plasma, with the plasma parameter k describing its effect on photon motion. The results reveal that the influence of the β parameter on the photon motion is significant near the black hole and it becomes weak at larger distances from the black hole. The deflection angle of photons for gravitational lensing which depends on the spin of the black hole demonstrates monotonic decrease with increase in the value of the plasma parameter k. The presence of the β parameter leads to a maximum deflection angle near the black hole, which decreases with increasing photon distance from the horizon of the black hole. The photon sphere radius is strongly affected by the β parameter and by the black hole spin, but weakly influenced by the plasma parameter. The shadow cast by the black hole which is altered by the β parameter, deformed on the left-hand side. Increase in the value of the plasma parameter k reduces the shadow size of the black hole. The effect of the spin on the shadow size is observed when β takes comparatively bigger values. The average shadow radius is affected by the spacetime parameters and plasma parameter, exhibiting a non-monotonic behavior with increasing β. The distortion of shadow of the black hole is influenced by the parameter β in a considerable and non-monotonic manner. Observational constraints for Sgr A* show our model aligns within confidence bounds but falls short of upper limits, revealing shadow radius limitations.

Effect of electric interaction on the deflection and gravitational lensing in the strong field limit

The deflection angle Delta phi of charged signals in general charged spacetime in the strong deflection limit is analyzed in this work using a perturbative method generalized from the neutral signal case. The solved Delta phi naturally contains the finite distance effect and takes a quasi-power series form with a logarithmic divergence at the leading order. The coefficients of the series contain both the gravitational and electric contributions. Using the Reissner–Nordström spacetime as an example, we found that an electric repulsion (or attraction) tends to decrease (or increase) the critical impact parameter b_c. If the repulsion is strong enough, then b_c can shrink to zero and the critical particle sphere r_{0c} will disappear. These results are applied to the gravitational lensing of charge signal, from which we solved the image positions, their magnifications and time delays. It is found that in general, the electric repulsion (or attraction) will decrease (or increase) the image apparent angles, the black hole shadow sizes as well as their magnifications but increase (or decrease) the time delays.