Related papers: Euclidean Algorithm for a Gravitational Lens in a …

We study analytically a gravitational lens due to a deformed star, which is modeled by using a monopole and a quadrupole moment. Positions of the images are discussed for a source on the principal axis. We present explicit expressions for…

Gravitational lensing is the deflection of light rays due to the gravity of intervening masses. This phenomenon is observed in a variety of scales and configurations, involving any non-uniform mass such as planets, stars, galaxies, clusters…

We develop a semi - analytical method to reconstruct the lensing potential in quadruply imaged gravitational lens systems. Assuming that the potential belongs to a broad class of boxy non - elliptical models, we show how it is possible to…

The purpose of this paper is twofold. An immediate practical use of the presented algorithm is its applicability to the parametric solution of underdetermined linear ordinary differential equations (ODEs) with coefficients that are…

This paper reviews a phenomenological approach to the gravitational lensing by exotic objects such as the Ellis wormhole lens, where exotic lens objects may follow a non-standard form of the equation of state or may obey a modified gravity…

We recall Labatie's effective method of solving polynomial equations with two unknowns by using the Euclidean algorithm.

The number of strong lens systems is expected to increase significantly in ongoing and upcoming surveys. With an increase in the total number of such systems we expect to discover many configurations that correspond to unstable caustics. In…

Two exact lens equations have been recently shown to be equivalent to each other, being consistent with the gravitational deflection angle of light from a source to an observer, both of which can be within a finite distance from a lens…

The gravitational lensing signal produced by a galaxy or a galaxy cluster is determined by its total matter distribution, providing us with a way to directly constrain their dark matter content. State-of-the-art numerical simulations…

Based on the geodesic equation in a static spherically symmetric metric we discuss the rotation curve and gravitational lensing. The rotation curve determines one function in the metric without assuming Einstein's equations. Then lensing is…

A variational principle is applied to 4D Euclidean space provided with a tensor refractive index, defining what can be seen as 4-dimensional optics (4DO). The geometry of such space is analysed, making no physical assumptions of any kind.…

Gravitational lensing refers to the deflection of light by the gravity of celestial bodies, often predominantly composed of dark matter. Seen through a gravitational lens, the images of distant galaxies appear distorted. In this paper we…

Gravitational lensing allows us to probe the structure of matter on a broad range of astronomical scales, and as light from a distant source traverses an intervening galaxy, compact matter such as planets, stars, and black holes act as…

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…

If an extended source, such as a galaxy, is gravitationally lensed by a massive object in the foreground, the lensing distorts the observed image. It is straightforward to simulate what the observed image would be for a particular lens and…

We discuss the effects of an isolated gravitational lens on the rotation of the plane of polarization of linearly polarized light rays, the so called gravitational Faraday rotation, in metric theories of gravity. By applying the thin lens…

We study gravitational lensing by quadrupole potentials within the linearized gravity approximation and the integration over the unperturbed photon trajectory. It is well known that the quadrupole potential contribution to the deviation…

This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…

Keeping the exact general relativistic treatment of light bending as a reference, we compare the accuracy of commonly used approximate lens equations. We conclude that the best approximate lens equation is the Ohanian lens equation, for…

In this work, we present our classification algorithm to identify strong gravitational lenses from wide-area surveys using machine learning convolutional neural network; LensExtractor. We train and test the algorithm using a wide variety of…