Radius Of Photon Sphere Research Articles

Black holes, photon sphere, and cosmology in ghost-free [formula omitted] gravity

The improved version of ghost-free f(G) gravity introduced in Nojiri and Odintsov (2005) is proposed and investigated. It is demonstrated that improved ghost-free f(G) gravity may be consistently applied to describe the expanding universe (with horizon) as well as the static spacetime like black holes. Interestingly, such a theory looks like a close avatar of scalar-Einstein–Gauss–Bonnet gravity with the only difference that the scalar field is not a dynamical one so that many predictions of ghost-free f(G) gravity are very similar to that of sEGB gravity.We discuss the gravitational wave in the improved model with the condition that the propagating speed of the gravitational wave is identical to that of the propagation speed of light. A model that describes inflation in the early universe and could satisfy the observational constraints is also constructed. The solution of ghost-free f(G) gravity realising the given static spacetime with spherical symmetry is proposed. Some of such solutions realise explicitly the Reissner–Nordström black hole or the Hayward black hole, which is a regular black hole without curvature singularity, We also construct a black hole in our theory which contains the Arnowitt–Deser–Misner (ADM) mass, the horizon radius, and the radius of the photon sphere as independent parameters. The radius of the black hole shadow in this model as well as photon sphere radius are estimated. It is shown that there exists a parameter region which satisfies the constraints coming from Event Horizon Telescope observations. Furthermore, we construct model where the radius of the black hole shadow or photon orbit is smaller than the horizon radius supposed from the ADM mass.

Quasinormal modes, thermodynamics and shadow of black holes in Hu–Sawicki f(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{f(R)}$$\\end{document} gravity theory

We derive novel black hole solutions in a modified gravity theory, namely the Hu–Sawicki model of f(R) gravity. After obtaining the black hole solution, we study the horizon radius of the black hole from the metric and then analyse the dependence of the model parameters on the horizon. We then use the 6th order WKB method to study the quasinormal modes of oscillations (QNMs) of the black hole perturbed by a scalar field. The dependence of the amplitude and damping part of the QNMs are analysed with respect to variations in model parameters and the error associated with the QNMs are also computed. After that we study some thermodynamic properties associated with the black hole such as its thermodynamic temperature as well as greybody factors. It is found that the black hole has the possibility of showcasing negative temperatures and is thermodynamically unstable for feasible values of model parameters. Then we analyse the geodesics and derive the photon sphere radius as well as the shadow radius of the black hole. The photon radius is independent of the model parameters while shadow radius showed fair amount of dependence on the model parameters. We tried to constrain the parameters with the help of Keck and VLTI observational data and obtained some bounds on m and c2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$c_{2}$$\\end{document} parameters.

Photon orbits and phase transitions in Kiselev-AdS black holes from f(R,T)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(R,\\; T)$$\\end{document} gravity

The acceleration observed in cosmological expansion is often attributed to negative pressure, potentially arising from quintessence. We explore the relationship between the photon orbit radius and the phase transition of spherical AdS black holes in f(R, T) gravity influenced by quintessence dark energy, specifically Kiselev-AdS black holes in f(R, T) gravity. We are treating the negative cosmological constant Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document} as the system’s pressure to examine the impact of the state parameter ω\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega $$\\end{document} and the f(R, T) gravity parameter γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}. Interestingly, Kiselev-AdS black holes within the f(R, T) gravity framework exhibit a van der Waals-like phase transition. In contrast, these black holes display a Hawking–Page-like phase transition in general relativity. We demonstrate that below the critical point, the black hole undergoes a first-order vdW-like phase transition, with rps\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{ps}$$\\end{document} and ups\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{ps}$$\\end{document} serving as order parameters exhibiting a critical exponent of 1/2, similar to ordinary thermal systems. It suggests that rps\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$r_{ps}$$\\end{document} and ups\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$u_{ps}$$\\end{document} can serve as order parameters in characterizing black hole phase transitions, hinting at a potentially universal gravitational relationship near critical points within black hole thermodynamic systems. Investigating the correlation between photon sphere radius and thermodynamic phase transitions provides a valuable means of distinguishing between different gravity theory models, ultimately shedding light on the nature of dark energy. Finally, as γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document} tends towards zero, our results precisely align with those of Kiselev-AdS black holes.

Geodesics structure and deflection angle of electrically charged black holes in gravity with a background Kalb–Ramond field

This article investigates the geodesic structure and deflection angle of charged black holes in the presence of a nonzero vacuum expectation value background of the Kalb–Ramond field. Topics explored include null and timelike geodesics, energy extraction by collisions, and the motion of charged particles. The photon sphere radius is calculated and plotted to examine the effects of both the black hole charge (Q) and the Lorentz-violating parameter (b) on null geodesics. The effective potential for timelike geodesics is analyzed, and second-order analytical orbits are derived. We further show that the combined effects of Lorentz-violating parameter and electric charge can mimic a Kerr black hole spin parameter up to its maximum values, i.e., a/M∼1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a/M \\sim 1$$\\end{document} thus suggesting that the current precision of measurements of highly spinning black hole candidates may not rule out the effect of Lorentz-violating parameter. The center of mass energy of colliding particles is also considered, demonstrating a decrease with increasing Lorentz-violating parameter. Circular orbiting particles of charged particles are discovered, with the minimum radius for a stable circular orbit decreasing as both b and Q increase. Results show that this circular orbit is particularly sensitive to changes in the Lorentz-violating parameter. Additionally, a timelike particle trajectory is demonstrated as a consequence of the combined effects of parameters b and Q. Finally, the light deflection angle is analyzed using the weak field limit approach to determine the Lorentz-breaking effect, employing the Gauss–Bonnet theorem for computation. Findings are visualized with appropriate plots and thoroughly discussed.

Effect of dark energy on photon orbits and thermodynamic phase transition for Hayward anti-de Sitter black holes

We investigate a black hole solution analogous to Hayward regular black holes with a negative cosmological constant surrounded by quintessence — the Hayward–Kiselev anti-de Sitter (AdS) black hole, derived from Einstein equations coupled with nonlinear electrodynamics. The solution reveals a singularity due to the quintessential dark energy, and we have outlined the conditions necessary for regularity. When pressure, e.g., P=0.016, the effect of quintessential dark energy results in an otherwise absent van der Waal phase transition and second-order phase transition. Interestingly, the impact of dark energy decreases critical temperature (Tc), whereas critical pressure (Pc) increases. Investigating the correlation between photon sphere radius and the first-order phase transition exhibited non-monotonic behaviour among the photon sphere radius, nonlinear charge parameter, temperature, and pressure under certain conditions. Variations in the photon sphere radius and impact parameter before and after the phase transition serve as order parameters. The critical exponents Δrps and Δups near the critical point consistently approach 1/2, suggesting that rps and ups can be order parameters for black hole phase transitions and indicating a potential universal gravitational relationship near the critical point within a black hole thermodynamic system. We also analysed the previously unexplored Kiselev-AdS black hole, which emerges as a particular case in the limit g→0.

Shadows, rings and optical appearance of a magnetically charged regular black hole illuminated by various accretion disks

Abstract The Event Horizon Telescope (EHT) imaging of the supermassive black holes at the centers of Messier 87 galaxy (M87) and the Milky Way galaxy (Sgr A) marks a significant step in observing the photon rings and central brightness depression that define the optical appearance of black holes with an accretion disk scenario. Inspired by this, we take into account a static and spherically symmetric magnetically charged regular black hole (MCRBH) metric characterized by its mass and an additional parameter q, which arises from the coupling of Einstein gravity and nonlinear electrodynamics (NLED) in the weak field approximation. This parameterized model offers a robust foundation for testing the coupling of Einstein gravity and NLED in the weak-field approximation, using the EHT observational results. In this study, we investigate the geodesic motion of particles around the solution, followed by a discussion of its fundamental geometrical characteristics such as scalar invariants. Using null geodesics, we examine how the model parameter influences the behavior of the photon sphere radius and the associated shadow silhouette. We seek constraints on q by applying the EHT results for supermassive black holes M87* and Sgr A*. Furthermore, it is observed that the geodesics of time-like particles are susceptible to variations in q, which can have an impact on the traits of the innermost stable circular orbit and the marginally bounded orbit. Our primary objective is to probe how the free parameter q affects various aspects of the accretion disk surrounding the MCRBH using the thin-disk approximation. Next, we discuss the physical characteristics of the thin accretion disk as well as the observed shadows and rings of the MCRBH, along with its luminosity, across various accretion models. Ultimately, variations in accretion models and the parameter q yield distinct shadow images and optical appearances of the MCRBH.

The gravitational lensing by rotating black holes in loop quantum gravity

In this paper, we explore gravitational lensing effects associated with rotating black holes within the framework of loop quantum gravity. Utilizing the Gauss-Bonnet theorem as extended by Ono et al., we compute the light deflection angle in the weak field limit for a lens that is finitely distanced from both the source and the observer. Our findings indicate that the weak deflection angle for rotating black holes in LQG is smaller than that observed for the classical Kerr black holes, albeit with minimal deviations. In the strong field limit, we determine the photon sphere radius, the light deflection angle, and lensing observables, including the image position θ∞, angular separation s, magnification rmag, and temporal delays among various relativistic images. By considering supermassive black holes, such as Sgr A* and M87*, within the LQG framework, we calculate these observables and investigate the influence of the quantum parameter Aλ on them, compared with the Kerr black hole outcomes. Our comparative analysis reveals that the image position θ∞ and separation s for Sgr A* consistently exceed those for M87*, whereas M87* exhibits considerably greater time delays than Sgr A*. These distinctions could be important in differentiating between rotating black holes in LQG and classical Kerr black holes in future astronomical observations.

Dynamical photon spheres in charged black holes and naked singularities

To understand the nature of a black hole shadow in dynamical spacetimes, we construct an analytical model of a dynamical photon sphere in the context of the Bonnor–Vaidya spacetime. Comparing the resulting photon sphere radius with the one in Vaidya spacetime, we find that the charge always decreases the radius of the photon sphere. We also prove that a naked singularity in Bonnor–Vaidya spacetime, unlike the static Reissner–Nordstrom naked singularity, may cast a shadow, and as a result, it cannot be distinguished from a black hole through its shadow.

General approach on shadow radius and photon spheres in asymptotically flat spacetimes and the impact of mass-dependent variations

Recent observations of black hole shadows have revolutionized our ability to probe gravity in extreme environments. This manuscript presents a novel analytic method to calculate, in leading-order terms, the key parameters of photon sphere and shadow radius. This method offers advantages for complex metrics where traditional approaches are cumbersome. We further explore the impact of black hole mass on the photon sphere radius, providing insights into black hole interactions with their surroundings. Our findings contribute significantly to black hole physics and gravity under extreme conditions. By leveraging future advancements in observations, such as the next-generation Event Horizon Telescope (ngEHT), this work paves the way for even more precise tests of gravity near black holes.

Analyzing the influence of geometrical deformation on photon sphere and shadow radius: A new analytical approach — Spherically symmetric spacetimes

In this paper, we introduce a new approach to study the behavior of the photon sphere and shadow radius. Our method uses extended gravitational decoupling and reveals two important analytic results. First, the additional matter field alters the photon sphere radius: it increases if g′(rph(0))>0 and decreases if g′(rph(0))<0 (where g′ represents the derivative of a specific metric function evaluated at the original photon sphere radius). Second, the presence of the matter field can modify the black hole shadow size. If grph(0)>0, the shadow shrinks, while it grows for grph(0)<0. These findings provide a deeper insight into how matter distribution influences the characteristics of black holes and their observable features. Through a systematic framework and various illustrative examples, our investigation not only clarifies these fundamental aspects but also significantly enhances the theoretical framework of black hole astrophysics.

Quasi-periodic oscillations and particle motion around charged black hole surrounded by a cloud of strings and quintessence field in Rastall gravity

This work mainly focuses on unveiling the particle dynamics features of black holes. For this objective, we utilize the charged black hole geometry consisting of the cloud strings and quintessence under the ansatz of Rastall gravity. We have calculated and analyzed the effective potential, angular momentum, particle energy, horizon radius, inner stable circular orbit, photon sphere radius, quasi-periodic oscillations, and effective force to reveal the dynamical features. We in detail discussed the effects of charge in black hole, Rastall parameter, strings of cloud parameter, and quintessential parameter on the calculated results. To ensure the scenario of accelerated expansion, ω q lies in the range −1 < ω q < −1/3. From this specific range, we choose ω q = −2/3.

Photon orbits and phase transition for Letelier AdS black holes immersed in perfect fluid dark matter

Abstract We obtain an exact solution of spherically symmetric Letelier AdS black holes immersed in perfect fluid dark matter (PFDM). Considering the cosmological constant as the positive pressure of the system and volume as its conjugate variable, we analyse the thermodynamics of our black holes in the extended phase space. Owing to the background clouds of strings parameter ($a$) and the parameter endowed with PFDM ($\beta$), we analyse the Hawking temperature, entropy and specific heat. We also investigate the relationship between the photon sphere radius and the phase transition for the Letelier AdS black holes immersed in PFDM. Through the analysis, we find with a particular condition, there are non-monotonic behaviours between the photon sphere radius, the impact parameter, the PFDM parameter, temperature, and pressure. We can regard both the changes of photon sphere radius and impact parameter before and after phase transition as the order parameter; their critical exponents near the critical point are equal to the same value 1/2, just like ordinary thermal systems. These indicate that a universal relation of gravity may exist near the critical point for a black hole thermodynamic system.

Light trajectories and thermal shadows casted by black holes in a cavity

We explore the shadows and the photon rings casted by black holes in cavity. Placing theobserver inside such an isothermal background, we examine the influence of the cavitytemperature T cav and the charge Q on the involved optical features. Afterstudying the effect of the horizon radius by varying Q, we investigate the thermalbehaviors of the black hole shadows in a cavity. For fixed charge values, we find that theshadow radius r s increases by decreasing T cav. Varying such a temperature, wediscuss the associated energy emission rate. After that, we show that the curves in the r s-T cav plane share similarities with the G-T curves of the Anti de Sitter blackholes. Then, we study the trajectories of the light rays casted by black holes in a cavity.We further observe that the light trajectory behaviors are different than the ones of thenon rotating black holes due to the cavity effect. Finally, we provide an evidence for theexistence of an universal ratio defined in terms of the photon sphere radius and the impactparameter. Concretely, we obtain an optical ratio b sp/r sp∼√(3).

Thermal stability and effects of thermal fluctuations on the static and spherically symmetric hairy black hole by gravitational decoupling

In this paper, we explore the thermodynamic aspects of the hairy black hole solution developed by gravitational decoupling in the spherical symmetry, considering its energy emission, Gibbs free energy, and thermal fluctuations. Our analysis involves the calculation of various quantities, including the Hawking temperature, geometric mass, and heat capacity to discuss the thermodynamic stability at local and global scales. To determine the temperature of the black hole, we utilize the first law of thermodynamics. Additionally, we evaluate the energy emission rate and establish its proportionality to the decoupling parameter α. By calculating the Gibbs free energy, we investigate the phase transition behavior through the swallowing tails of the hairy black holes. Furthermore, we derive the corrected entropy to examine the impact of thermal fluctuations on small and large black holes. We also calculated horizon radius r0, inner stable circular orbit rISCO , photon sphere radius rph, and shadows radius Rsh. Remarkably, the length scale parameters α (decoupling parameter) and β exhibit substantial influences on the thermodynamic properties of under consideration hairy black holes.

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.

Testing metric-affine gravity using particle dynamics and photon motion

This work mainly focuses to unveil the optical features of a black hole. For this objective, we utilize the metric-affine black hole geometry, including dilation, spin, and shear charge. The Lagrangian coefficients f1 and d1 are the main parameters that differentiate the solutions by d1=±8f1, where f1<0. Based on these parameters, we carry out this work in two cases, i.e., d1=8f1,&d1=−8f1. We forecast the detailed impact of dilation, spin, and shear charges on the optical properties of black hole in both cases. To reveal the optical features, we calculate horizon radius, inner stable circular orbit, photon sphere radius, BH shadows, quasi-periodic oscillations, the red-blue shift of photon particles, effective force, weak gravitational lensing, and image magnification by using metric-affine gravity black hole geometry.

Strong lensing and shadow of Ayon-Beato–Garcia (ABG) nonsingular black hole

We study nonsingular black holes viewed from the point of view of Ayon-Beato–Garcia (ABG) nonlinear electrodynamics (NLED) and present a complete study of their corresponding strong gravitational lensing. The NLED modifies the the photon’s geodesic, and our calculations show that such effect increases the corresponding photon sphere radius and image separation, but decreases the magnification. We also show that the ABG’s shadow radius is not compatible with bound estimates of Sgr A* from Keck and VLTI (Very Large Telescope Interferometer). Thus, the possibility of Sgr A* being a nonsingular ABG black hole is ruled out.

Shadows and strong gravitational lensing by Van der Waals black hole in homogeneous plasma

In this paper, we first analyze the horizon structure of the Van der Waals (VdW) black hole and then investigate its shadow in the absence of a plasma medium as well as the presence of a homogeneous plasma medium. We find that both the Van der Waals parameters a and b have a significant effect on the shadow of the black hole. We also observe that the radius of the shadow in a homogeneous plasma medium increases when parameter σ=ωpω∞ (the ratio of plasma frequency and photon frequency) increases and the radius of the shadow inhomogeneous plasma medium is larger than the vacuum medium. We also discuss the strong gravitational lensing in a homogeneous plasma medium. We observe that the photon sphere radius, deflection limit coefficients and deflection angle in the strong field are highly affected by the presence of a homogeneous plasma medium. We also find that the deflection angle in the strong field limit by the Van der Waals black hole with the homogeneous plasma is greater than that of the Vacuum medium. Further, we discuss the observable quantities angular position θ∞, separation S and magnification rmag by taking the example of a supermassive black hole M87∗ in the context of Van der Waals black hole and compared to the other ordinary black hole such as Schwarzschild Ads black hole in the strong field limit with the effects of homogeneous plasma. It is concluded that the Van der Waals parameters a, b and homogeneous plasma medium have a significant effect on both the shadows and strong gravitational lensing. It is further concluded that the Van der Waals black hole can be quantitatively distinguished from the other ordinary black hole such as Schwarzschild Ads black hole via shadow and strong lensing observations.

Testing symmergent gravity through the shadow image and weak field photon deflection by a rotating black hole using the M87^* and Sgr. hbox {A}^* results

In this paper, we study rotating black holes in symmergent gravity, and use deviations from the Kerr black hole to constrain the parameters of the symmergent gravity. Symmergent gravity induces the gravitational constant G and quadratic curvature coefficient c_{textrm{O}} from the flat spacetime matter loops. In the limit in which all fields are degenerate in mass, the vacuum energy V_{textrm{O}} can be wholly expressed in terms of G and c_{textrm{O}}. We parametrize deviation from this degenerate limit by a parameter {hat{alpha }} such that the black hole spacetime is dS for {hat{alpha }} < 1 and AdS for {hat{alpha }} > 1. In constraining the symmergent parameters c_{textrm{O}} and {hat{alpha }}, we utilize the EHT observations on the M87* and Sgr. A* black holes. We investigate first the modifications in the photon sphere and shadow size, and find significant deviations in the photonsphere radius and the shadow radius with respect to the Kerr solution. We also find that the geodesics of time-like particles are more sensitive to symmergent gravity effects than the null geodesics. Finally, we analyze the weak field limit of the deflection angle, where we use the Gauss-Bonnet theorem for taking into account the finite distance of the source and the receiver to the lensing object. Remarkably, the distance of the receiver (or source) from the lensing object greatly influences the deflection angle. Moreover, c_{textrm{O}} needs be negative for a consistent solution. In our analysis, the rotating black hole acts as a particle accelerator and possesses the sensitivity to probe the symmergent gravity.

The eye of the storm: Optical properties

Investigation of the optical properties of a black hole described by the so-called “eye of the storm” space–time has been the main aim of the work. Such a space–time is regular and recovers the Minkowski space–time at asymptotical infinity due to the effect of the so-called “suppression parameter” involved in the metric. It has been shown that an increase in the suppression parameter reduces the inclination angle of photons in the close regions around a black hole due to gravitational lensing. Investigation of the photon motion has also shown that bigger values of this parameter reduce the photon sphere radius as well. It has been also detected that the shape of a black hole shadow is affected in the presence of the suppression parameter and the bigger values of this parameter twist the shape of a shadow stronger. Lastly, it has been demonstrated that the average shadow radius is bigger for smaller suppression parameters and the distortion of the shape of shadow from a circle is bigger for bigger suppression parameters and bigger spin of a black hole.