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In this work are reviewed several aspects of gravitational lensing produced by astrophysical bodies that strongly curve the spacetime in their vicinity. When an object with a photon sphere (e.g. a black hole) is interposed between a source…

General Relativity and Quantum Cosmology · Physics 2014-09-15 Ernesto F. Eiroa

Deflection of light by gravity was predicted by General Relativity and observationaly confirmed in 1919. In the following decades various aspects of the gravitational lens effect were explored theoretically, among them the possibility of…

Astrophysics · Physics 2015-06-24 Joachim Wambsganss

One of the most fascinating predictions of the theory of general relativity is the effect of gravitational lensing, the bending of light in close proximity to massive stellar objects. Recently, artificial optical materials have been…

Optics · Physics 2013-10-01 C. Sheng , H. Liu , Y. Wang , S. N. Zhu , D. A. Genov

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds…

Astrophysics of Galaxies · Physics 2014-11-20 A. O. Petters , M. C. Werner

When the gravitational lensing potential can be approximated by that of circularly symmetric system affected by weak perturbations, it is found that the shape of the resulting (tangential) caustics is entirely specified by the local…

Astrophysics · Physics 2007-05-23 Jin H. An

Gravitational lensing provides an efficient tool for the investigation of matter structures, independent of the dynamical or hydrostatic equilibrium properties of the deflecting system. However, it depends on the kinematic status. In fact,…

Astrophysics · Physics 2009-11-13 M. Sereno

The specified constant 4-vector field reproducing the spherically symmetric stationary metric of cold dark matter halo in the region of flat rotation curves results in a constant angle of light deflection at small impact distances. The…

General Relativity and Quantum Cosmology · Physics 2009-11-11 V. V. Kiselev , D. I. Yudin

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

The influence of plasma on different effects of gravitational lensing is reviewed. Using the Hamiltonian approach for geometrical optics in a medium in the presence of gravity, an exact formula for the photon deflection angle by a black…

General Relativity and Quantum Cosmology · Physics 2015-07-31 G. S. Bisnovatyi-Kogan , O. Yu. Tsupko

The basic concepts of gravitational microlensing are introduced. We start with the lens equation, and then derive the image positions and magnifications. The statistical quantities of optical depth and event rate are then described. We…

Astrophysics · Physics 2008-11-05 Shude Mao

We found strong similarities between the gravitational lensing and the conventional optical lensing. The similarities imply a graded refractive index description of the light deflection in gravitational field. We got a general approach to…

General Relativity and Quantum Cosmology · Physics 2009-11-13 Xing-Hao Ye , Qiang Lin

We revisit the gravitational lensing of light or gravitational waves by Schwarzschild black hole in geometric optics. Instead of a single massless particle, we investigate the collective behavior of a congruence of light/gravitational rays,…

General Relativity and Quantum Cosmology · Physics 2025-02-11 Zhao Li , Xiao Guo , Tan Liu , Tao Zhu , Wen Zhao

Gravitational lensing of a gamma ray burst (GRB) by a single point mass will produce a second, delayed signal. Several authors have discussed using microlensed GRBs to probe a possible cosmological population of compact objects. We analyse…

Astrophysics · Physics 2009-10-31 J. S. B. Wyithe , E. L. Turner

We present a framework that reformulates gravitational lensing as an optical phenomenon governed by an effective refractive index, enabling exploration of modified gravity theories using undergraduate-level mathematics and optics. After…

General Relativity and Quantum Cosmology · Physics 2026-04-09 Romy Hanang Setya Budhi

Gravitational lensing describes the bending of the trajectories of light and gravitational waves due to the gravitational potential of a massive object. Strong lensing by galaxies can create multiple images with different overall…

General Relativity and Quantum Cosmology · Physics 2024-02-26 Simon M. C. Yeung , Mark H. Y. Cheung , Joseph A. J. Gais , Otto A. Hannuksela , Tjonnie G. F. Li

We investigate the effect of the redshift drift in strong gravitational lensing. The redshift drift produces a time variation of $i)$ the apparent position of a lensed source and $ii)$ the time delay among incoming signals from different…

Cosmology and Nongalactic Astrophysics · Physics 2017-05-17 Oliver F. Piattella , Leonardo Giani

Luminous tracers have been used extensively to map the large-scale matter distribution in the Universe. Similarly the dynamics of stars or galaxies can be used to estimate masses of galaxies and clusters of galaxies. However, assumptions…

Cosmology and Nongalactic Astrophysics · Physics 2016-11-25 H. Hoekstra

These lectures give an introduction to Gravitational Lensing. We discuss lensing by point masses, lensing by galaxies, and lensing by clusters and larger-scale structures in the Universe. The relevant theory is developed and applications to…

Astrophysics · Physics 2009-09-25 Ramesh Narayan , Matthias Bartelmann

Gravitational lensing is the phenomenon arising when light rays are deflected by the mass between the source and the observer. Largely magnified and highly distorted images of background galaxies are formed by these angular deflections if…

Cosmology and Nongalactic Astrophysics · Physics 2025-07-02 Atınç Çağan Şengül

We offer a concise and direct way to derive the bending angle of light (i.e. as generally called, gravitational lensing), while light grazes a star, through the approach suggested earlier by the first author, which is fundamentally based on…

General Physics · Physics 2014-01-15 Tolga Yarman , Alexander Kholmetskii , Metin Arik