Black Hole Shadow Research Articles

The shadows of quintessence non-singular black hole

In 2022, the Event Horizon Telescope (EHT) collaboration has reported the first observations of Sagittarius A*(SgrA*). Applying the EHT observational results, we find out constraints on non-singular Hayward parameter of regular dark energy black hole. Considering these constraints and different thin disk accretion, we present a detailed investigation into influence of different dark energy and Hayward parameters on shadows from non-singular Hayward black holes. In the first second-order attenuation function model, corresponding shadow radius and peak for observed intensity from direct image decrease with increasing dark energy parameter and Hayward parameter. However, for the lensing ring and photon ring, corresponding peak become bigger as dark energy parameter increase in case of fixed Hayward parameter. In the second third-order attenuation function model, significantly different from model 1, above two rings completely overlay on the direct image, resulting in two distinct peaks in the observed intensity. As increase of Hayward and dark energy parameters, the difference between the two peaks decreases, and shadows and observed intensity decrease. In the final inverse trigonometric function attenuation model, the result shows corresponding lensing ring as well as photon ring can be distinguished within the superposition region, and the superposition region becomes larger. With the increase of the dark energy parameter, the shadow radius exhibits a decreasing trend, while observed intensity increases. However, with the increase of the Hayward parameter, both decreases. Compared with the first two models, the shadow radius becomes smaller, but the observed intensity becomes larger, making the bright ring wider and brighter. Therefore, different accretion models and non-singular Hayward parameters can give rise to interesting and distinguish characteristic for the black hole shadow and rings.

Exploring the quintessential influence on shadows of black holes in Finsler-Hayward geometry

This research aims to shed light on how the quintessential dark energy influences the shadows cast by black holes by considering different kinds of surrounding accretion profiles within the framework of Finsler-Hayward geometry. We explore the impact of the Finsler parameter (η) and the quintessence parameter (ω) on fundamental properties of the black hole, such as its horizons, photon sphere, and impact parameter. By examining the observed characteristics of the black hole's shadow, including the photon ring and shadow intensities, we analyze how the quintessence affects these features under varying scenarios of matter accretion. Leveraging observational data from the Event Horizon Telescope, exclusively focusing on celestial bodies such as Sgr A* and M87*, we narrow down the range of the Finsler parameter (η) within our model of quintessence-infused Finsler Hayward black holes. By comparing our findings with models such as Finsler Schwarzschild, with and without the quintessence Finsler Hayward black holes, we observe that the quintessence's influence on the black hole's shadow surpasses the effects attributed to regularity. This study contributes to our insight into how the Finsler parameter and the quintessence of dark energy shape the shadows of black holes in diverse accretion environments, shedding light on their intricate nature and behavior, particularly in the context of Finsler Hayward geometry.

Four STU black holes shadows

Abstract In this work, we examine the optical behaviors and thermodynamic phase structures using shadow analysis for four S T U black holes. The study is conducted for four cases of charge configurations on the parameter space M ( q 1 , q 2 , q 3 , q 4 ) . As a matter of fact, both the electric charge as a parameter and the parameter space M ( q 1 , q 2 , q 3 , q 4 ) affect the geometry of the black hole shadow, particularly the size of the shadow. We also introduce a constraint on the charge of the black hole from the observational results of the M87 ⋆ and Sgr A ⋆ shadow. Furthermore, we show that the electric charge and the parameter space M ( q 1 , q 2 , q 3 , q 4 ) have a non-trivial impact on the variation of the energy emission rate. Interestingly enough, we find novel scenarios in which the evaporation is slower, which causes the lifetime of the black holes to be considerably elongated. On the other side, the phase structure of four S T U black holes is explored for two cases of electric charge configuration. The findings show a perfect correlation between the shadow and event horizon radii. This correlation is, in fact, helpful in discovering the phase transition in terms of the shadow radius. In addition, the microstructure is being analyzed in terms of shadow analysis, providing similar behavior to the ordinary situation of the Ruppeiner formalism.

Shadow and gravitational weak lensing for quantum improved charged black hole in plasma* *Supported partly 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

We investigated the shadow and weak gravitational lensing for the quantum-improved charged black hole (BH). First, the photon motion and BH shadow were studied in a plasma medium. It can be seen from our analysis that the radius of the photon sphere of the quantum-improved charged BH and size of the BH shadow decrease under the influence of the plasma parameter . Furthermore, the gravitational weak lensing is considered for the quantum-improved charged BH, and we have obtained the deflection angle of light rays around a compact object for uniform and non-uniform plasma cases. It is shown that the value of the deflection angle for uniform plasma increases with increasing plasma parameter, and vice versa for non-uniform plasma. It has been also indicated that under the influence of the plasma parameter and BH charge , the values of the deflection angles for the two cases decrease. Finally, we investigated the magnification of image brightness using the deflection angle of the light rays around the quantum-improved charged BH.

Shadow and quasinormal modes of novel charged rotating black hole in Born–Infeld theory: Constraints from EHT results

This work investigates the shadow and quasinormal modes of a novel rotating Born–Infeld-type black hole. First, we study the effect of interaction between nonlinear electrodynamic fields and photons on shadow radius and show that it is less than the error of shadow measurements in Event Horizon Telescope (EHT) observations. Then, we obtain a rotating metric using the Newman–Janis algorithm, starting with the initial metric of the nonrotating novel Born–Infeld black hole solution. Next, we analyze the null geodesics to determine the celestial coordinates. The black hole’s shadow radius is determined by using celestial coordinates. The mass, spin, charge, and nonlinearity parameters all influence the shape and size of the black hole shadow. An increase in the spin parameter results in a gradual reduction in the size of black hole shadows and further distortion of the shadows. Furthermore, constraints on the spin and electric charge of black holes, as well as the nonlinearity parameter, are derived through the utilization of the shadow sizes of supermassive black holes Sagittarius (Sgr) A* and M87* obtained from observations of the EHT. Also, we investigate the correlation between the standard shadow radius and the equatorial and polar quasinormal modes for revolving black holes. Finally, we analyze the emission energy rate from the black hole based on different spacetime parameters. Our observation indicates that the emission energy rate decreases as the values of spin and nonlinearity parameters increase, keeping the charge-to-mass ratios of the Born–Infeld black hole constant.

Higher-dimensional MOG dark compact object: shadow behaviour in the light of EHT observations

Consideration of extra spatial dimensions is motivated by the unification of gravity with other interactions, the achievement of the ultimate framework of quantum gravity, and fundamental problems in particle physics and cosmology. Much attention has been focused on the effect of these extra dimensions on the modified theories of gravity. Analytically examining astrophysical phenomena like black hole shadows is one approach to understand how extra dimensions would affect the modified gravitational theories. The purpose of this study is to derive a higher-dimensional metric for a dark compact object in STVG theory and then examine the behaviour of the shadow shapes for this solution in STVG theory in higher dimensions. We apply the Carter method to formulate the geodesic equations and the Hamilton–Jacobi method to find photon orbits around this higher-dimensional MOG dark compact object. We investigate the effects of extra dimensions and the STVG parameter 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} on the black hole’s shadow size. Next, we compare the shadow radius of this higher-dimensional MOG dark compact object to the shadow size of the supermassive black hole M87*, which has been realized by the Event Horizon Telescope (EHT) collaborations, in order to restrict these parameters. We find that extra dimensions in the STVG theory typically lead to a reduction in the shadow size of the higher-dimensional MOG dark compact object, whereas the effect of parameter 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} on this black hole’s shadow is suppressible. Remarkably, given the constraints from EHT observations, we find that the shadow size of the four-dimensional MOG dark compact object lies in the confidence levels of the EHT data. Finally, we investigate the issue of acceleration bounds in higher-dimensional MOG dark compact object in confrontation with EHT data of M87*.

Kerr-MOG-(A)dS black hole and its shadow in scalar-tensor-vector gravity theory

The scalar-tensor-vector gravity (STVG) theory has attracted significant interest due to its ability to effectively address the issue of galaxy rotation curves and clusters of galaxies without considering the influence of dark matter. In this paper, we construct rotating black hole solutions with a cosmological constant in the STVG theory (i.e., Kerr-MOG-(A)dS black hole solutions), where the import of a gravitational charge as a source modifies the gravitational constant, determined by GG = G N(1+α). For Kerr-MOG-dS spacetime, the observer is situated at a specific location within the domain of outer communication, rather than being located infinitely far away. Since black hole shadows are shaped by light propagation in spacetime, the interaction between the MOG parameter and the cosmological constant is expected to produce novel effects on these shadows. As the cosmological constant Λ increases, the apparent size of the black hole shadow decreases. Additionally, the shadow expands with an increase in the MOG parameter α, reaching a maximum at a certain value, and its shape becomes more rounded under an arbitrary rotation parameter, which leads to degeneracy between different black hole parameters. However, by employing numerical ray-tracing techniques, we have found that gravitational lensing and the frame-dragging effect effectively distinguish this degeneracy. Our work contributes to a deeper understanding of black holes in modified gravity, their observational signatures, and constraints.

Shadow of Kerr black hole surrounded by a cloud of strings in Rastall gravity and constraints from M87*

Motivated by the first image of a black hole captured by the Event Horizon Telescope (EHT), there has been a surge of research using observations of black hole shadows to test theories of gravity. In this paper, we carry out a study related to the shadow of Kerr black holes surrounded by a cloud of strings in Rastall gravity, which deviates from the Kerr black hole due to the presence of the string parameter a0 and the parameter β. The horizons, ergospheres, and photon region of the black hole are shown. Moreover, we explore the shadow and observations of the black hole, which are closely linked to the parameters a0 and β. By treating M87* as a Kerr black hole surrounded by a cloud of strings under Rastall gravity, we constrain the black hole parameters using the EHT observations. For a given β, the circularity deviation of the black hole obeys ΔC≲0.1 in all regions. The angular diameter θd=42±3μas provides the upper bound of parameters a and a0 for fixed β. The shadow axis ratio satisfies the observation data of EHT (1<Dx≲4/3) in the whole space for a given β. These results are consistent with the public information from EHT. In other words, candidates for real astrophysical black holes can be Kerr black holes surrounded by a cloud of strings in Rastall gravity.

Study of deflection angle and shadow in supergravity black hole theory under the influence of non-magnetic plasma medium

In this paper, we examine models of a black hole’s deflection angle in the context of gauged super-gravity, using the black hole’s optical metric. We compute Gaussian curvature and the Gauss-Bonnet theorem of optical metric and also follow the Gibbons-Werner technique to calculate the deflection angle. The spacetime curvature effects are significant and will have extensive implications for gauged supergravity theory. By incorporating the Gaussian curvature of the optical metric over a four-dimensional surface of light dispersion. Further, we examine the deflection angle in the presence of the non-magnetic plasma medium and how the non-magnetic plasma impacts the deflection angle. Furthermore, we show how the photon sphere influences the gauged supergravity and non-magnetized plasma of the black hole shadow, as well as how to generate black hole shadows by employing the ray tracing approach. Finally, we analyze the shadow cast and address plots of both the deflection angle and the shadow to understand the deflection angle functions and the shadow impact in the non-magnetic plasma medium.

Shadow and quasinormal modes of rotating charged black holes in Kalb–Ramond gravity and implications from EHT data

The recent observations of the Event Horizon Telescope for the supermassive black holes M87* and Sgr A* can potentially test gravity theories and acquire further knowledge on black holes and gravity parameters. An essential field of research focuses on the shadow and quasinormal modes of black holes. Therefore, we used the Newman–Janis algorithm to get a rotating charged black hole solution in Kalb–Ramond gravity. Then, we looked at the event horizon radius, the static limit, and the ergoregion of spacetime. We derive the null geodesic equations and the effective potential for photon radial motion. We also investigate how the black hole’s Kalb–Ramond, spin, and charge parameters affect the shadow size and distortion. It is obtained that an increase in the Kalb–Ramond parameter causes a decrease in the radius and increases the distortion of the shadow size. We obtain constraints on black hole charge and spin using the data obtained from Event Horizon Telescope observations of M87* and Sgr A* by testing the effects of the Kalb–Ramond gravity parameter. We examine the energy emission rate using Hawking radiation and demonstrate that a rise in the Kalb–Ramond parameter diminishes this rate. Finally, we calculated and analyzed the typical shadow radius, equatorial, and polar quasinormal modes using the geometric–optic connection between quasinormal mode parameters and conserved quantities along geodesics.

Note on black holes with kilometer-scale ultraviolet regulators

Regular black hole metrics involve a universal, mass-independent regulator that can be up to O(700km) while remaining consistent with terrestrial tests of Newtonian gravity and astrophysical tests of general relativistic orbits. However, for such large values of the regulator scale, the metric describes a compact, astrophysical-mass object with no horizon rather than a black hole. We note that allowing the regulator to have a nontrivial mass dependence preserves the horizon, while allowing large, percent-level effects in black hole observables. By considering the deflection angle of light and the black hole shadow, we demonstrate this possibility explicitly.

A comparison between the deflection angles of massive and massless particles in the Schwarzschild space-time and their consequences on black hole shadows

In this paper, we present comparisons of the deflection angles of massless and massive particles in the Schwarzschild space-time. For the case of photons in a general static space-time, we construct a spatial 3D equation of motion for their path that leads to an implicit formula for the deflection angle. We then compare our results with well-known results of the literature in the Schwarzschild space-time. For the case of massive particles, we calculate the deflection angle only in the Schwarzschild space-time. The end result is that as the velocity of any massive particle diminishes, the deflection angle increases. To show the relevance of these comparisons, we constructed different black hole shadows for massive particles in order to be compared with a shadow made by photons.

A regular MOG black hole’s impact on shadows and gravitational weak lensing in the presence of a quintessence field

We investigate the impact of the modified gravity (MOG) field and the quintessence scalar field on horizon evolution, black hole (BH) shadow and the weak gravitational lensing around a static spherically symmetric BH. We first begin to write the BH metric associated with the MOG parameter and quintessence scalar field. We then determine the BH shadow and obtain numerical solutions for the photon sphere and shadow radius. We show that the MOG (α) and the quintessence (c) parameters have a significant impact on the BH shadow and photon sphere. Based on the analysis, we further show that the combined effects of the MOG parameter and quintessence field can increase the values of BH shadow and photon sphere radii. We also obtain constraints on the BH parameters by applying the observational data of Sgr A⋆ and M87⋆. Finally, we consider the weak deflection angle of BH within the context of the Gauss–Bonnet theorem (GBT) and show that the combined effects of the MOG and quintessence parameters do make the value of the deflection angle increase, and find this remarkable property is in good agreement with the physical meaning of both parameters that can maintain the strong gravitational field in the surrounding environment of a BH.

Analytical perturbations of relativistic images in Kerr space-time

Light rays passing very close to black holes may wind several times before escaping. For any given electromagnetic source around the black hole, a distant observer would thus observe two infinite sequences of images on either side of the black hole. These images are generated by light rays performing an increasing numbers of loops. The strong deflection limit provides a simple analytic formalism to describe such higher order images for spherically symmetric metrics, while for axially symmetric black holes one typically resorts to numerical approaches. Here we present the leading order perturbation to higher order images when the black hole spin is turned on. We show that the images slide around the black hole shadow as an effect of space-time dragging. We derive analytical formulae for their shifts and the perturbation of their time delays. We also discuss how such simple analytical formulae for images by Kerr black holes can be of great help in many applications.

Constraints on quasinormal modes from black hole shadows in regular non-minimal Einstein Yang–Mills gravity

This work deals with scalar quasinormal modes using the higher-order WKB method and black hole shadow in non-minimal Einstein–Yang–Mills theory. To validate the results of quasinormal modes, time domain profiles are also investigated. We find that with an increase in the magnetic charge of the black hole, the ringdown gravitational wave increases non-linearly and the damping rate decreases non-linearly. The presence of a magnetic charge also results in a non-linear decrease in the black hole shadow. For large values of the coupling parameter, the black hole becomes a soliton solution and the corresponding ringdown gravitational wave frequency increases slowly with a decrease in the damping rate. For the soliton solutions, the shadow is also smaller. The constraints on the model parameters calculated using shadow observations of M87* and Sgr A* and an approximate analytical relation between quasinormal modes and shadows at the eikonal limit are discussed.

Timelike bound orbits and pericenter precession around black hole with conformally coupled scalar hair

We investigate the geodesic motions of timelike particles around a static hairy black hole with conformally coupled scalar field. We mainly focus on the effects of the scalar charge and electric charge on the marginally bound orbits (MBO), innermost stable circular orbits (ISCO) and on the precessing orbits around this black hole. Our results show that both the scalar and electric charges suppress the energy as well as the angular momentum of the particles in the bound orbits. Then, we study the relativistic periastron precessions of the particles and constrain the charge parameters by employing the observational result of the S2 star’s precession in SgrA*. It is found that the constraints on the charge parameters from S2 star’s motion are tighter than those from black hole shadow. Finally, we analyze the periodic motions of the particles and figure out samples of periodic orbits’ configurations around the hairy black hole.

Shadows and weak gravitational lensing for black holes within Einstein-Maxwell-scalar theory* *Supported by the National Natural Science Foundation of China (11675143), and the National Key Research and Development Program of China (2020YFC2201503). M.A and B.A wish to acknowledge the support from Research Grant F-FA-2021-432 of the Ministry of Higher Education, Science and Innovations of the Republic of Uzbekistan.

In this study, we investigated the optical properties of charged black holes within the Einstein-Maxwell-scalar (EMS) theory. We evaluated the shadow cast by these black holes and obtained analytical solutions for both the radius of the photon sphere and that of the shadow. We observed that black hole parameters γ and β both influence the shadow of black holes. We also found that the photon sphere and shadow radius increase as a consequence of the presence of the parameter γ. Interestingly, the shadow radius decreases first and then remains unchanged owing to the impact of the parameter β. Finally, we analyzed the weak gravitational lensing and total magnification of lensed images around black holes. We found that the charge of the black holes and the parameter β both have a significant impact, reducing the deflection angle. Similarly, the same behavior for the total magnification was observed, also as a result of the effect of the charge of the black holes and the parameter β.

Einstein-Grisaru-Zanon gravity

The leading (α′)3-correction to the gravitational low-energy effective action of closed (type II) superstring theory in four-spacetime dimensions defines the Einstein-Grisaru-Zanon gravity action that is applied for a calculation of the leading corrections to the Schwarzschild solution and the Hubble function in the Friedmann-Lemaitre-Robertson-Walker universe, in the first order with respect to the effective string-generated coupling. The solutions found are compared to the corresponding solutions in the Einstein-Bel-Robinson gravity that also modifies the Einstein gravity by the terms quartic in the spacetime curvature. We consider the black hole shadows in the Einstein-Grisaru-Zanon gravity theory and derive the upper bound on the string coupling parameter from the Hawking temperature of a black hole.

Constraining photon trajectories in black hole shadows

We examine the shadow cast by a Kerr black hole, focusing on constraints on photons corresponding to different shadow boundaries. The photons are related to different orbital ranges and impact parameter values, creating a map of the shadow boundaries. Our analysis fixes also the conditions under which it is possible to observe an “imprint” of the black hole (outer) ergosurface and (outer) ergoregion on the Kerr black hole shadow boundary. The counter-rotating case resulted strongly constrained with respect to the co-rotating case, constituting a remarkable and significant difference where the counter-rotating component associated with the shadow boundary is strongly distinct from the co-rotating one. However, in this framework, even the co-rotating photons imply restrictions on conditions on the spins and planes, which are bounded by limiting values. We believe the results found here, being a tracer for the central black hole, can constitute new templates for the ongoing observations.

Vacuum spacetime with multipole moments: The minimal size conjecture, black hole shadow, and gravitational wave observables

Vacuum spacetime with multipole moments: The minimal size conjecture, black hole shadow, and gravitational wave observables