Strong gravitational lensing by a charged Kiselev black hole

We study the gravitational lensing scenario where the lens is a spherically symmetric charged black hole (BH) surrounded by quintessence matter. The null geodesic equations in the curved background of the black hole are derived. The resulting trajectory equation is solved analytically via perturbation and series methods for a special choice of parameters, and the distance of the closest approach to black hole is calculated. We also derive the lens equation giving the bending angle of light in the curved background. In the strong field approximation, the solution of the lens equation is also obtained for all values of the quintessence parameter \(w_q\). For all \(w_q\), we show that there are no stable closed null orbits and that corrections to the deflection angle for the Reissner–Nordström black hole when the observer and the source are at large, but finite, distances from the lens do not depend on the charge up to the inverse of the distances squared. A part of the present work, analyzed, however, with a different approach, is the extension of Younas et al. (Phys Rev D 92:084042, 2015) where the uncharged case has been treated.     

Strong field gravitational lensing by a stringy charged black hole

In this paper, we study gravitational lensing of magnetically charged black hole of string theory as a strong field approximation for the supermassive black hole at the center of NGC4486B. We evaluate light deflection angle numerically, from which we obtain magnifications, Einstein rings and observables for the relativistic images. Finally, we explore time delay between relativistic images when they are on the same as well as opposite side of the lens. It is concluded that charge parameter plays a prominent role in the strong gravitational lensing.     

Center-of-mass energy for the Plebanski-Demianski black hole

We study the center-of-mass energy of the particles colliding in the vicinity of acceleration and event horizons of the Plebanski and Demianski class of black holes. We calculate the collision energy of uncharged particles in the center-of-mass frame that are freely falling along the equatorial plane of a charged accelerating and rotating black hole with an NUT parameter. This energy turns out to be infinite in the non-extremal case, while in the extremal case, it becomes infinitely large near the event horizon only if the particle has the critical angular momentum. We conclude that the center-of-mass energy depends on the rotation and the NUT parameter.     

Strong gravitational lensing for photon coupled to Weyl tensor in Kiselev black hole

The objective of the present work is to highlight the phenomena of strong gravitational lensing and deflection angle for the photon coupling with the Weyl tensor in a Kiselev black hole. Here, we have extended the prior work of Chen and Jing (S. Chen and J. Jing, JCAP, 10: 002 (2015)) for a Schwarzschild black hole to a Kiselev black hole. For this purpose, the equation of motion for the photons coupled to the Weyl tensor, null geodesic, and equation of photon sphere in a Kiselev black hole spacetime have been formulated. It is found that the equation of motion of the photons depends not only on the coupling between the photons and the Weyl tensor, but also on the polarization direction of the photons. There is a critical value of the coupling parameter, \begin{document}$ \alpha$\end{document} , for the existence of the marginally circular photon orbit outside the event horizon, which depends on the parameters of the black hole and the polarization direction of the photons. Further, the polarization directions of the coupled photons and the coupling parameter, \begin{document}$ \alpha$\end{document}; both modify the features of the photon sphere, angle of deflection, and functions \begin{document}$ (\bar{a}$\end{document} and \begin{document}$ \bar{b})$\end{document} owing to the strong gravitational lensing in the Kiselev black hole spacetime. In addition to this, the observable gravitational lensing quantities and the shadows of the Kiselev black hole spacetime are presented in detail.     

Vacuum polarization near a black hole creating particles

The renormalized expectation value of the energy-momentum tensor associated with scalar massless particles created by a Schwarzschild black hole is calculated by performing a numerical computation.     

Thermodynamic equilibrium and heavy particles near a black hole

Some consequences of black-hole thermodynamics are examined     

Weak gravitational lensing of Dilaton-de Sitter black holes

In this work, we examine the effects of the cosmological constant and a scalar field on the angle of deflection of null geodesics in the equatorial plane of the Dilaton-de Sitter space–time. We employ the Rindler–Ishak method to compute the gravitational lensing. We derive new limits on the value of the cosmological constant, \(\Lambda \), based on the bending of light by systems where the lens is a distant galaxy or a cluster of galaxies. These results are essential and important for studies of cosmology.     

Particle motion and gravitational lensing in the metric of a dilaton black hole in a de Sitter universe

We consider the metric exterior to a charged dilaton black hole in a de Sitter universe. We study the motion of a test particle in this metric. Conserved quantities are identified and the Hamilton–Jacobi method is employed for the solutions of the equations of motion. At large distances from the black hole the Hubble expansion of the universe modifies the effective potential such that bound orbits could exist up to an upper limit of the angular momentum per mass for the orbiting test particle. We then study the phenomenon of strong field gravitational lensing by these black holes by extending the standard formalism of strong lensing to the non-asymptotically flat dilaton-de Sitter metric. Expressions for the various lensing quantities are obtained in terms of the metric coefficients.     

Strong gravitational lensing by regular electrically charged black holes

In nonlinear electrodynamics a photon does not follow null geodesics of background geometry, but moves along null geodesics of a corresponding effective geometry. Therefore, in the strong deflection limit, in order to study the gravitational lensing of the regular electrically charged black holes obtained by coupling general relativity to nonlinear electrodynamics, one should firstly obtain the corresponding effective geometry, which is a necessary and key step. I obtain the deflection angle of the photon in the strong deflection limit, and further calculate the angular position and magnification of relativistic images. It is found that, the electric charge has significant effect on the gravitational lensing of regular black holes. With the increase of the electric charge q, the angular position of the relativistic images \(\theta _{\infty }\) and the relative magnification \(\mathcal {R}_{m}\) as a function of q decrease, while the angular separation between the outermost relativistic image and the others \(\mathcal {S}\) as a function of q increases. I also discuss the measurement of observables for the black hole at the center of our Galaxy in the cases of regular electrically charged black hole effective metrics.     

Extreme gravitational lensing in vicinity of Schwarzschild-de Sitter black holes

We have developed a realistic, fully general relativistic computer code to simulate optical projection in a strong, spherically symmetric gravitational field. The standard theoretical analysis of optical projection for an observer in the vicinity of a Schwarzschild black hole is extended to black hole spacetimes with a repulsive cosmological constant, i.e, Schwarzschild-de Sitterspacetimes. Influence of the cosmological constant is investigated for static observers and observers radially free-falling from the static radius. Simulations include effects of the gravitational lensing, multiple images, Doppler and gravitational frequency shift, as well as the intensity amplification. The code generates images of the sky for the static observer and a movie simulations of the changing sky for the radially free-falling observer. Techniques of parallel programming are applied to get a high performance and a fast run of the BHC simulation code.      

Particle dynamics,black hole shadow and weak gravitational lensing in the f(Q) theory of gravity

We study the particle dynamics around a black hole(BH) in f(Q) gravity. First, we investigate the influence of the parameters of f(Q) gravity on the horizon structure of the BH, photon orbits and the radius of the innermost stable circular orbit(ISCO) of massive particles. We further study the effects of the parameters of f(Q) gravity on the shadow cast by the BH. Moreover, we consider weak gravitational lensing using the general method, where we also explore the deflection angle of light rays a...     

Shadow thermodynamics of the Hayward-AdS black hole

In this paper, the phase structure of the Hayward-anti-de Sitter(AdS) black hole(BH) is studied using shadow formalism. It has been found that the shadow radius is a monotonic function of the horizon radius and can therefore play an equivalent role to the horizon radius in characterizing the thermodynamics of the Hayward-AdS BH. The thermodynamic phase transition(PT) of the Hayward-AdS BH is investigated with the shadow radius. It is shown that as the magnetic charge increases, the shadow radius...     

Effects of acceleration on the collision of particles in the rotating black hole spacetime

We study the collision of two geodesic particles in the accelerating and rotating black hole spacetime and probe the effects of the acceleration of black hole on the center-of-mass energy of the colliding particles and on the high-velocity collision belts. We find that the dependence of the center-of-mass energy on the acceleration in the near event-horizon collision is different from that in the near acceleration-horizon case. Moreover, the presence of the acceleration changes the shape and position of the high-velocity collision belts. Our results show that the acceleration of black holes brings about richer physics for the collision of particles.     

Magnetised black hole as a gravitational lens

We use the Ernst–Schwarzschild solution for a black hole immersed in a uniform magnetic field to estimate corrections to the bending angle and time delay due-to presence of weak magnetic fields in galaxies and between galaxies, and also due-to influence of strong magnetic field near super-massive black holes. The magnetic field creates a kind of confinement in space, that leads to increasing of the bending angle and time delay for a ray of light propagating in the equatorial plane.     

Gravitational lensing of a star by a rotating black hole

The gravitational lensing of a finite star moving around a rotating Kerr black hole has been numerically simulated. Calculations for the direct image of the star and for the first and second light echoes have been performed for the star moving with an orbital period of 3.22 h around the supermassive black hole SgrA* at the center of the Galaxy. The time dependences for the observed position of the star on the celestial sphere, radiation flux from the star, frequency of detected radiation, and major and minor semiaxes of the lensed image of the star have been calculated and plotted. The detailed observation of such lensing requires a space interferometer such as the Russian Millimetron project.     

Formation of black hole and emission of gravitational waves

Numerical simulations were performed for the formation process of rotating black holes. It is suggested that Kerr black holes are formed for wide ranges of initial parameters. The nature of gravitational waves from a test particle falling into a Kerr black hole as well as the development of 3D numerical relativity for the coalescing binary neutron stars are discussed.     

String dynamics near a black hole

The dynamics of a string near a Kaluza-Klein black hole are studied. Solutions to the geodesic equations are obtained using the world sheet velocity of light as an expansion parameter. For a string falling into a magnetically charged black hole, it is shown that the compact dimension decreases with the world-sheet coordinate τ.