Related papers: Accurate analytic formula for light bending in Sch…
We obtain an approximate solution for the motion of a charged particle around a Schwarzschild black hole immersed in a weak dipolar magnetic field. We focus on eccentric bound orbits in the equatorial plane of the Schwarzschild black hole…
Bending of light rays by gravitational sources is one of the first evidences of the general relativity. When the gravitational souce is a stationary massive object such as a black hole, the bending angle has an integral representation, from…
Gravitational lensing is one of the most impressive celestial phenomena, which has interesting behaviors in its strong field limit. Near such limit, Bozza finds that the deflection angle of light is well-approximated by a logarithmic term…
Numerical integration of the differential equations of light propagation in the Schwarzschild metric shows that in some situations relevant for practical observations the well-known post-Newtonian solution for light propagation has an error…
We present here a detailed derivation of an explicit spin-dependent expression for the bending angle of light as it traverses in the equatorial plane of a spinning black hole. We show that the deflection produced in the presence of the…
In this paper, we investigate the gravitational lensing effect and the shadow around a Schwarzschild-like black hole in metric-affine bumblebee gravity, which leads to the Lorentz symmetry breaking. We first present a generalized formalism…
We describe a new approach to calculating photon trajectories and gravitational lensing effects in the strong gravitational field of the Kerr black hole. These techniques are applied to explore both the imaging and spectral properties of…
In this work we derive novel analytical expressions for the mass and distance of a Schwarzschild black hole (BH), as well as for the orbital radius of test particles orbiting it, it terms of astrophysical observables measured throughout the…
We deduce a new formula for the perihelion advance of a test particle in the Schwarzschild black hole by applying a newly developed non-linear transformation within the Schwarzschild space-time. By this transformation we are able to apply…
Deflection angles of massive test particles moving along an unbound trajectory in the Schwarzschild metric are considered for the case of large deflection. We analytically consider the strong deflection limit, which is opposite to the…
We calculate the photon sphere $r_{ph}$ and critical curve $b_c$ for the quantum corrected Schwarzschild black hole, finding that they violate an universal inequalities proved for asymptotically flat black holes which satisfy null energy…
We consider the velocity shift of light in presence of radiation emitted by a black body. Within geometric optics formalism we calculate the bending angle of a light ray when there is a gradient in the energy density. We model the bending…
An exact solution is obtained for the gravitational bending of light in static, spherically symmetric metrics which includes the Schwarzschild-de Sitter spacetime and also the Mannheim-Kazanas metric of conformal Weyl gravity. From the…
We examine the motion of an electron constrained to follow a magnetic field line near a primordial sub-stellar mass black hole. Earlier studies treated the problem in flat (Minkowski) spacetime, yielding qualitatively correct results and…
Both massless light ray and objects with nonzero mass experience trajectory bending in a gravitational field. In this work the bending of trajectories of massive objects in a Schwarzschild spacetime and the corresponding gravitational…
Explicit expressions for the bending angle of light deflection arising from phenomenologically deformed black-hole metrics, subject to possible weak and strong quantum gravity effects, respectively, are obtained, by a highly effective…
Using Weierstrassian elliptic functions the exact geodesics in the Schwarzschild metric are expressed in a simple and most transparent form. The results are useful for analytical and numerical applications. For example we calculate the…
In the present work, we theoretically investigate gravitational lensing in the spacetime of a holonomy corrected Schwarzschild black hole. Analytical expressions for the light deflection angle are obtained in both the weak field limit and…
In this paper we study the gravitational lensing effect for the Schwarzschild solution with holonomy corrections. We use two types of approximation methods to calculate the deflection angle, namely the weak and strong field limits. For the…
A generalized lens equation for weak gravitational fields in Schwarzschild metric and valid for finite distances of source and observer from the light deflecting body is suggested. The magnitude of neglected terms in the generalized lens…