Related papers: A comparison of approximate gravitational lens equ…
We first define what we mean by gravitational lensing equations in a general space-time. A set of exact relations are then derived that can be used as the gravitational lens equations in all physical situations. The caveat is that into…
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…
An exact analytical expression for the bending angle of light due to a non-rotating massive object, considering the actual distances from source and observer to the gravitational mass, is derived. Our novel formula generalizes Darwin…
We study approximate solutions of the gravitational lens equation and corresponding lens magnification factor near the critical point. This consideration is based on the Taylor expansion of the lens potential in powers of coordinates and an…
It is shown that the lens equation for a binary gravitational lens being a set of two coupled real fifth-order algebraic equations (equivalent to a single complex equation of the same order) can be reduced to a single real fifth-order…
This is a general work on gravitational lensing. We present new expressions for the optical scalars and the deflection angle in terms of the energy-momentum tensor components of matter distributions. Our work generalizes standard references…
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…
Gravitational lensing has developed into one of the most powerful tools for the analysis of the dark universe. This review summarises the theory of gravitational lensing, its main current applications and representative results achieved so…
We develop an iterative approach to gravitational lensing theory based on approximate solutions of the null geodesic equations. The approach can be employed in any space-time which is ``close'' to a space-time in which the null geodesic…
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…
The theory of gravitational lensing is reviewed from a spacetime perspective, without quasi-Newtonian approximations. More precisely, the review covers all aspects of gravitational lensing where light propagation is described in terms of…
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…
Lensing in a spherically symmetric and static spacetime is considered, based on the lightlike geodesic equation without approximations. After fixing two radius values r_O and r_S, lensing for an observation event somewhere at r_O and static…
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…
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…
The basic equations and geometry of gravitational lensing are described, as well as the most important contexts in which it is observed in astronomy: strong lensing, weak lensing and microlensing.
Predictions of the standard thin lens approximation and a new iterative approach to gravitational lensing are compared with an ``exact'' approach in simple test cases involving one or two lenses. We show that the thin lens and iterative…
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…
We give the lens equation for light deflections caused by point mass condensations in an otherwise spatially homogeneous and flat universe. We assume the signal from a distant source is deflected by a single condensation before it reaches…
We reformulate the transport equation which determines the size, shape and orientation of infinitesimal light beams in arbitrary spacetimes. The behaviour of such light beams near vertices and conjugate points is investigated, with special…