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General relativistic deflection of light by mass, dipole, and quadrupole moments of gravitational field of a moving massive planet in the Solar system is derived in the approximation of the linearized Einstein equations. All terms of order…

General Relativity and Quantum Cosmology · Physics 2007-12-05 Sergei Kopeikin , Valeri Makarov

In this letter we apply the Gauss--Bonnet theorem (GB) to calculate the deflection angle by a quantum corrected Schwarzschild black hole in the weak limit approximation. In particular we calculate the light deflection by two types of…

General Relativity and Quantum Cosmology · Physics 2017-06-09 Kimet Jusufi

In this paper we investigate the strong gravitational lensing with Gauss-Bonnet gravity. By considering the logarithmic term for deflection angle, we obtain the deflection angle $\hat\alpha$ and corresponding parameters $\bar{a}$ and…

General Relativity and Quantum Cosmology · Physics 2015-06-17 J. Sadeghi , H. Vaez

Here the gravitational lensing in strong field limit of a Schwarzschild black hole with a solid deficit angle owing to global monopole within the context of the $f(R)$ gravity theory is investigated. We obtain the expressions of deflection…

General Relativity and Quantum Cosmology · Physics 2015-09-23 Jingyun Man , Hongbo Cheng

The deflection of light rays near gravitating objects can be influenced not only by gravity itself but also by the surrounding medium. Analytical studies of such effects are possible within the geometrical optics approximation, where the…

General Relativity and Quantum Cosmology · Physics 2025-12-03 Christian Pfeifer , Barbora Bezděková , Oleg Yu. Tsupko

We study the weak gravitational lensing effect of Non-Bocharova-Bronnikov-Melnikov-Bekenstein (BBMB) black hole in new massive conformal gravity. We analyze the deflection angle of light caused by new massive conformal gravity by using the…

General Relativity and Quantum Cosmology · Physics 2023-06-14 Muhammad Yasir , Xia Tiecheng , Farzan Mushtaq , Kazuharu Bamba

Gravitational lensing constitutes one of the most direct observational manifestations of spacetime curvature and provides a powerful probe of compact astrophysical objects. In this work, we present a comprehensive analysis of the bending of…

General Relativity and Quantum Cosmology · Physics 2026-04-21 Partha Pratim Basumallick , Saheb Das , Bhaswati Mandal , Subhadip Sau

In this paper, we study the gravitational lensing by some black hole classes within the non-linear electrodynamics in weak field limits. First, we calculate an optical geometry of the non-linear electrodynamics black hole then we use the…

General Relativity and Quantum Cosmology · Physics 2022-03-22 H. El Moumni , K. Masmar , Ali Övgün

The deflection and gravitational lensing of light and massive particles in arbitrary static, spherically symmetric and asymptotically (anti-)de Sitter spacetimes are considered in this work. We first proved that for spacetimes whose metric…

General Relativity and Quantum Cosmology · Physics 2021-10-13 Zixiao Li , Haotian Liu , Junji Jia

The gravitational deflection angle of light for an observer and source at finite distance from a lens object has been studied by Ishihara et al. [Phys. Rev. D, 94, 084015 (2016)], based on the Gauss-Bonnet theorem with using the optical…

General Relativity and Quantum Cosmology · Physics 2020-05-27 Keita Takizawa , Toshiaki Ono , Hideki Asada

We show with the help of Fermat's principle that every lightlike geodesic in the NUT metric projects to a geodesic of a two-dimensional Riemannian metric which we call the optical metric. The optical metric is defined on a (coordinate) cone…

General Relativity and Quantum Cosmology · Physics 2021-03-25 Mourad Halla , Volker Perlick

In order to clarify effects of the finite distance from a lens object to a light source and a receiver, the gravitational deflection of light has been recently reexamined by using the Gauss-Bonnet (GB) theorem in differential geometry…

General Relativity and Quantum Cosmology · Physics 2019-11-07 Toshiaki Ono , Hideki Asada

In this paper, we investigate various key aspects of a static and spherically symmetric black hole with global monopole. Firstly, we analyze the deflection angle in the strong field limit of massive particle by the global monopole. It shows…

General Relativity and Quantum Cosmology · Physics 2026-04-08 Irengbam Roshila Devi , Ningthoujam Media , Yenshembam Priyobarta Singh , Telem Ibungochouba Singh

The deflection of light in the gravitational field of a massive body can be analyzed through diverse theoretical approaches. The null geodesic approach is commonly employed to calculate light deflection within strong and weak field limits.…

General Relativity and Quantum Cosmology · Physics 2026-04-14 Saswati Roy , Shubham Kala , Atanu Singha , Hemwati Nandan , A. K. Sen

In this paper, we study the weak gravitational deflection angle of relativistic massive particles by the Kerr-like black hole in the bumblebee gravity model. In particular, we focus on weak field limits and calculate the deflection angle…

General Relativity and Quantum Cosmology · Physics 2020-01-23 Zonghai Li , Ali Övgün

We study the deflection of light by a magnetic dipole field in the generalized Born-Infeld electrodynamics. Using the effective index of refraction and the trajectory equation based on geometric optics, we compute the weak bending angle of…

General Relativity and Quantum Cosmology · Physics 2022-07-06 Jin Young Kim

In this paper, using the recent method proposed by Ono, Ishihara and Asada (OIA) who extend the idea of Gibbons and Werner to the stationary and axisymmetric case, we apply the Gauss-Bonnet theorem to the optical metric of the non-rotating…

General Relativity and Quantum Cosmology · Physics 2018-08-23 Ali Övgün

We calculate the deflection of a light ray caused by the gravitational field of a cosmic string loop in the weak field limit and reduce the problem to a single quadrature over a time slice of the loop's world sheet. We then apply this…

Astrophysics · Physics 2011-09-09 Andrew A de Laix , Tanmay Vachaspati

It is known that a relative translational motion between the deflector and the observer affects gravitational lensing. In this paper, a lens equation is obtained to describe such effects on actual lensing observables. Results can be easily…

Astrophysics · Physics 2008-11-26 M. Sereno

We pursue a geometrical approach to gravitational lensing theory. We present a survey of the background theory of General Relativity, including particular properties of the Schwarzschild and Kerr solutions. Next we outline a proof of the…

Mathematical Physics · Physics 2011-11-22 Cameron Bloomer