Shadow images and observed luminosity of the Bardeen black hole surrounded by different accretions

In this paper, by exploring photon motion in the region near a Bardeen black hole, we studied the shadow and observed properties of the black hole surrounded by various accretion models. We analyzed the changes in shadow imaging and observed luminosity when the relevant physical parameters are changed. For the different spherical accretion backgrounds, we find that the radius of shadow and the position of the photon sphere do not change, but the observed intensity of shadow in the infalling accretion model is significantly lower than that in the static case. We also studied the contribution of the photon rings, lensing rings and direct emission to the total observed flux when the black hole is surrounded by an optically thin disk accretion. Under the different forms of the emission modes, the results show that the observed brightness is mainly determined by direct emission, while the lensing rings will provide a small part of the observed flux, and the flux provided by the photon ring is negligible. By comparing our results with the Schwarzschild spacetime, we find that the existence or change of relevant status parameters will greatly affect the shape and observed intensity of the black hole shadow. These results support the theory that the change of state parameter will affect the spacetime structure, thus affecting the observed features of black hole shadows.     

Shadows and observational appearance of a new family of Ayón-Beato-García black holes

In this paper, we study the shadows and observational appearance of the Ayón-Beato-García (ABG) black hole, which is surrounded by a thin disk accretion. For a four-dimensional ABG black hole, as the charge q increases, the event horizon r₊, radius r_p and impact parameter b_p of the photon sphere decrease, while the maximum value of effective potential V_eff increases. However, as the term γ associated with nonlinear electrodynamics increases, the related physical quantities r₊, r_p and b_p increase, but the maximum value of V_eff decreases. When the light ray reaches the vicinity of the ABG black hole, one can observe the trajectories of the light rays appearing as three types, i.e., direct emission, lens ring and photon ring. Furthermore, the shadows and the observational appearance of the ABG black hole are studied. The results show that the charge q and the term γ have a great influence on the shape and intensity of the black hole shadow. When the relevant state parameters change or the emission model changes, it can be argued that it is the direct emission that plays a decisive role in the total observed intensity of the ABG black hole, while the contribution of the lens ring to the total observed intensity is small and the photon ring makes almost no contribution.     

Shadow and photon sphere of black hole in clouds of strings and quintessence

In this study, we investigate the shadow and photon sphere of the black bole in clouds of strings and quintessence with static and infalling spherical accretions. We obtain the geodesics of the photons near a black hole with different impact parameters b to investigate how the string cloud model and quintessence influence the specific intensity by altering the geodesic and the average radial position of photons. In addition, the range of the string cloud parameter a is constrained to ensure that a shadow can be observed. Moreover, the light sources in the accretion follow a normal distribution with an attenuation factor γ, and we adopt a model of the photon emissivity \begin{document}$ j(\nu_e) $\end{document} to obtain the specific intensities. Furthermore, the shadow with static spherical accretion is plotted, which demonstrates that the apparent shape of the shadow is a perfect circle, and the value of γ influences the brightness of the photon sphere. Subsequently, we investigate the profile and specific intensity of the shadows with static and infalling spherical accretions, respectively. The interior of the shadows with an infalling spherical accretion will be darker than that with the static spherical accretion, and the specific intensity with both static and infalling spherical accretions gradually converges.     

Effect of nonlinear electrodynamics on shadows of slowly rotating black holes

In this study, we investigate the effect of nonlinear electrodynamics on the shadows of charged, slowly rotating black holes with the presence of a cosmological constant. Rather than the null geodesic of the background black hole spacetime, the trajectory of a photon, as a perturbation of the nonlinear electrodynamic field, is governed by an effective metric. The latter can be derived by analyzing the propagation of a discontinuity of the electromagnetic waveform. Subsequently, the image of the black hole and its shadow can be evaluated using the backward ray-tracing technique. We explore the properties of the resultant black hole shadows of two different scenarios of nonlinear electrodynamics, namely, the logarithmic and exponential forms. In particular, the effects of nonlinear electrodynamics on the optical image are investigated, as well as the image's dependence on other metric parameters, such as the black hole spin and charge. The resulting black hole image and shadow display rich features that potentially lead to observational implications.     

Chaotic shadows of black holes: a short review

We give a brief review on the formation and the calculation of black hole shadows. Firstly, we introduce the concept of a black hole shadow and the current works on a variety of black hole shadows. Secondly, we present the main methods of calculating photon sphere radius and shadow radius, and then explain how the photon sphere affects the boundary of black hole shadows. We review the analytical calculation for black hole shadows which have analytic expressions for shadow boundary due to the integrable photon motion system. And we introduce the fundamental photon orbits which can explain the patterns of black hole shadow shape. Finally, we review the numerical calculation of black hole shadows with the backward ray-tracing method and introduce some chaotic black hole shadows with self-similar fractal structures. Since the gravitational waves from the merger of binary black holes have been detected, we introduce a couple of shadows of binary black holes, which all have eyebrowlike shadows around the main shadows with the fractal structures. We discuss the invariant phase space structures of the photon motion system in black hole space-time, and explain the formation of black hole shadow is dominated by the invariant manifolds of certain Lyapunov orbits near the fixed points.     

Shadows of magnetically charged rotating black holes surrounded by quintessence

In this work, we study the optical properties of a class of magnetically charged rotating black hole spacetimes. The black holes in question are assumed to be immersed in the quintessence field, and subsequently, the resulting black hole shadows are expected to be modified by the presence of dark energy. We investigate the photon region and the black hole shadow, especially their dependence on the relevant physical conditions, such as the quintessence state parameter, angular momentum, and magnetic charge magnitude. The photon regions depend sensitively on the horizon structure and possess intricate features. Moreover, from the viewpoint of a static observer, we explore a few observables, especially those associated with the distortion of the observed black hole shadows.     

Shadow of a noncommutative geometry inspired Ayón Beato García black hole

We introduce the noncommutative geometry inspired Ayón Beato García black hole metric and study various properties of this metric by which we try to probe the allowed values of the noncommutative parameter \(\vartheta \) under certain conditions. We then construct the shadow (apparent shape) cast by this black hole. We derive the corresponding photon orbits and explore the effects of noncommutative spacetime on them. We then study the effects of noncommutative parameter \(\vartheta \), smeared mass m(r), smeared charge q(r) on the silhouette of the shadow analytically and present the results graphically. We then discuss the deformation which arises in the shape of the shadow under various conditions. Finally, we introduce a plasma background and observe how the shadow behaves in this scenario.     

Circular geodesics and accretion disk in the spacetime of a black hole including global monopole

We study circular time-like geodesics in the spacetime of a black hole including global monopole. We show that when the range of parameter changed the properties of the circular geodesics and the radiation of accretion disks are different. It follows that the properties of the accretion disk around black hole including global monopole can be different from that of a disk around Schwarzschild black hole.     

黑洞阴影在SSD中的位置和形状

假设旋转的黑洞在标准吸积盘内,在吸积盘的内边界等于最后稳定轨道的情况下,画出黑洞阴影在吸积盘的图像.通过定性和定量分析黑洞的形状和位置,发现对于相同质量的黑洞,黑洞阴影的大小及形状与黑洞的自旋参量有关.旋转黑洞阴影的形状和位置与它的旋转轴是不对称的,通过研究旋转轴与黑洞阴影的位置关系来确定黑洞的质量中心的位置及黑洞的旋转参量.     

Kerr–Newman-AdS black hole surrounded by perfect fluid matter in Rastall gravity

The Rastall gravity is the modified Einstein general relativity, in which the energy-momentum conservation law is generalized to \(T^{\mu \nu }_{~~;\mu }=\lambda R^{,\nu }\). In this work, we derive the Kerr–Newman-AdS (KN-AdS) black hole solutions surrounded by the perfect fluid matter in the Rastall gravity using the Newman–Janis method and Mathematica package. We then discuss the black hole properties surrounded by two kinds of specific perfect fluid matter, the dark energy (\(\omega =-\,2/3\)) and the perfect fluid dark matter (\(\omega =-\,1/3\)). Firstly, the Rastall parameter \(\kappa \lambda \) could be constrained by the weak energy condition and strong energy condition. Secondly, by analyzing the number of roots in the horizon equation, we get the range of the perfect fluid matter intensity \(\alpha \), which depends on the black hole mass M and the Rastall parameter \(\kappa \lambda \). Thirdly, we study the influence of the perfect fluid dark matter and dark energy on the ergosphere. We find that the perfect fluid dark matter has significant effects on the ergosphere size, while the dark energy has smaller effects. Finally, we find that the perfect fluid matter does not change the singularity of the black hole. Furthermore, we investigate the rotation velocity in the equatorial plane for the KN-AdS black hole with dark energy and perfect fluid dark matter. We propose that the rotation curve diversity in Low Surface Brightness galaxies could be explained in the framework of the Rastall gravity when both the perfect fluid dark matter halo and the baryon disk are taken into account.     

Properties of a thin accretion disk around a rotating non-Kerr black hole

We study the accretion process in the thin disk around a rotating non-Kerr black hole with a deformed parameter and an unbound rotation parameter. Our results show that the presence of the deformed parameter ? modifies the standard properties of the disk. For the case in which the black hole is more oblate than a Kerr black hole, the larger deviation leads to the smaller energy flux, the lower radiation temperature and the fainter spectra luminosity in the disk. For the black hole with positive deformed parameter, we find that the effect of the deformed parameter on the disk becomes more complicated. It depends not only on the rotation direction of the black hole and the orbit particles, but also on the sign of the difference between the deformed parameter ?   and a certain critical value _?c${?}_c$. These significant features in the mass accretion process may provide a possibility to test the no-hair theorem in the strong-field regime in future astronomical observations.     

Ideal hydrodynamics outside and inside a black hole: Hamiltonian description in Painlevé-Gullstrand coordinates

We show that when the Painlevé-Gullstrand coordinates are used in their Cartesian version, the Hamiltonian of relativistic ideal hydrodynamics in the vicinity of a nonrotating black hole differs by only one simple term from the corresponding Hamiltonian in a flat spacetime. The interior region of the black hole is also described in a unified way, because there is no singularity on the event horizon in Painlevé-Gullstrand coordinates. We present the exact solution describing the steady accretion of extremely hard matter (? ∝ n ²) onto a moving black hole up to the central singularity. In the local induction approximation, we derive the equation of motion for a thin vortex filament against the background of such an accretion flow. We explicitly calculate the Hamiltonian for a fluid with an ultrarelativistic equation of state, ? ∝ n ^4/3, and solve the problem of a centrally symmetric steady flow of such matter.     

Hawking Radiation of Reissner-Nordstr<Emphasis Type="Italic">ö</Emphasis>m Black Hole in Electromagnetic Field with Einstein Tensor Corrections

In this paper, we have investigated the absorption probability and Hawking radiation of electromagnetic field while it coupling with Einstein tensor in the background of 4-dimensional Reissner-Nordström(RN) black hole spacetime. Our results indicate that the properties of the absorption probability and Hawking radiation depend not only on the coupling parameter, but also on the parity of the electromagnetic field, which is quite different from those of the usual electromagnetic field without coupling in the 4-dimensional spacetime.The absorption probability, power emission spectra and luminosity of Hawking radiation decreases with the increase of coupling parameter α when the coupled electromagnetic field have odd-parity, and increases with the increase of coupling parameter α when the coupled electromagnetic field have even-parity.     

Quasinormal Modes of the Planar Black Holes of a Particular Lovelock Theory

In this work, we study the scalar quasinormal modes of a planar black hole metric in asymptotic anti-de Sitter spacetime derived from a particular Lovelock theory. The quasinormal frequencies are evaluated by adopting the Horowitz-Hubeny method as well as a matrix formalism. Also, the temporal evolution of small perturbations is studied by using finite difference method. The roles of the dimension of the spacetime, the parameter of the metric k, as well as the temperature of the background black hole, are discussed. It is observed that the particular form of the metric leads to quasinormal frequencies whose real parts are numerically insignificant. The black hole metric is found to be stable against small scalar perturbations.     

Motion and collision of particles near Plebanski-Demianski black hole: Shadow and gravitational lensing

Here we consider accelerating and rotating charged Plebanski-Demianski (PD) class of black hole metric as a particle accelerator. We obtain the geodesic motions (timelike, null and spacelike) of particles in a non-equatorial plane around the PD black hole. We find the effective potential, energy, angular momentum, impact parameters, and discuss the circular orbit. We study the center of mass energy of two neutral particles falling from infinity to near the non-extremal horizons (event and Cauchy horizons), extremal horizon, accelerating horizons, and near the center of the PD black hole. Also, we study the collision of a particle and a massless photon. Then we find the center of mass energy due to the collision of two massless photons in the PD black hole background. We compute the redshift and blueshift of the emitted photons by massive particles while light signal travels along null geodesics towards the observer located far away from the source. We study the Penrose process, which occurs within the ergosphere, and examines the particle’s motion with its implications. Here, we analyze the PD black hole shadow’s apparent shape, which forms far away from the black hole. We study the possible visibility of the PD black hole through photon’s shadow and energy emission rate. We also investigate the effect on the shadow of the PD black hole in plasma for a distant observer. We study the strong gravitational lensing by PD black hole. Finally, we analyze the deflection angle, lens equation, position, magnification, Einstein ring and observables by taking the supermassive PD black hole in the Galaxy’s center.     

Photon sphere and phase transition of d-dimensional (d ≥ 5) charged Gauss-Bonnet AdS black holes

Motivated by recent work, nonmonotonic behaviors of photon sphere radius can be used to reflect black hole phase transition for Reissner-Nordström-AdS (RN-AdS) black holes, we study the case of five-dimensional charged Gauss-Bonnet-AdS black holes in the reduced parameter space. We find that the nonmonotonic behaviors of photon sphere radius still exist. Using the coexistence line calculated from P-V plane, we capture the photon sphere radius of saturated small and large black holes (the boundary of the coexistence phase), then illustrate the reduced coexistence region. The results show that, reduced coexistence region decreases with charge Q but increases with Gauss-Bonnet coefficient α. When the charge vanishes, reduced coexistence region does not vary with Gauss-Bonnet coefficient α any more. In this case, the Gauss-Bonnet coefficient α plays the same role as the charge of five-dimensional RN-AdS black holes. Also, the situation of higher dimension is studied in the end.     

Weak deflection angle and shadow cast by the charged-Kiselev black hole with cloud of strings in plasma

In this study, the gravitational deflection angle of photons in the weak field limit (or the weak deflection angle) and shadow cast by the electrically charged and spherically symmetric static Kiselev black hole (BH) in the string cloud background are investigated. The influences of the BH charge Q, quintessence parameter γ, and string cloud parameter a on the weak deflection angle are studied using the Gauss-Bonnet theorem, in addition to studying the influences on the radius of photon spheres and size of the BH shadow in the spacetime geometry of the charged-Kiselev BH in string clouds. Moreover, we study the effects of plasma (uniform and non-uniform) on the weak deflection angle and shadow cast by the charged-Kiselev BH surrounded by the clouds of strings. In the presence of a uniform/nonuniform plasma medium, an increase in the string cloud parameter a increases the deflection angle α. In contrast, a decrease in the BH charge Q decreases the deflection angle. Further, we observe that an increase in the BH charge Q causes a decrease in the size of the shadow of the BH. We notice that, with an increase in the values of the parameters γ and a, the size of the BH shadow increases, and therefore, the intensity of the gravitational field around the charged-Kiselev BH in string clouds increases. Thus, the gravitational field of the charged-Kiselev BH in the string cloud background is stronger than the field produced by the pure Reissner-Nordstrom BH. Moreover, we use the data released by the Event Horizon Telescope (EHT) collaboration, for the supermassive BHs M87* and Sgr A*, to obtain constraints on the values of the parameters γ and a.     

Kerr Black Hole in the Background of the Einstein Universe

The Vaidya-Einstein-Kerr (VEK) black hole which represents the spacetime of the Kerr black hole in a non-vacuum, asymptotically non-flat background is investigated. The energy-momentum tensor corresponding to this spacetime satisfies reasonable energy conditions. We study several properties of this black hole and compare and contrast them with those of the Kerr black hole. We investigate the effect of the background on the geometry of the event horizon by computing the equatorial and polar circumferences and determining the oblateness of the horizon. We find that the surface area of the VEK black hole gets nontrivially coupled to rotation in sharp contrast to the Kerr case. We show that the angular velocity of the VEK horizon goes up significantly as the background influence increases. By using the `equatorial tangential velocity' of the VEK horizon we classify the horizon and define the `limiting black hole' a generalization that contains the extreme Kerr black hole as a special case. Finally we investigate the Gaussian curvature and establish conditions for global embedding of the VEK black hole in Euclidean space.     

Kiselev黑洞的热力学性质和物质吸积特性

本文考虑带有黑洞视界和宇宙视界的Kiselev时空.研究以黑洞视界和宇宙视界为边界的系统的热力学性质.统一地给出了两个系统的热力学第一定律;在黑洞视界半径远小于宇宙视界半径的情况下,近似地计算了通过宇宙视界和黑洞视界的热能.然后,探讨Kiselev时空的物质吸积特性.在吸积能量密度正比于背景能量密度的条件下给出黑洞的吸积率,讨论了黑洞吸积率与暗能量态方程参数的关系.