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The Gibbons-Werner method for calculating deflection angles using the Gauss-Bonnet theorem and optical/Jacobi metric has become widely popular in recent years. Werner extended this method to stationary spacetimes, where the optical/Jacobi…
In gravitational lensing, the usual viewpoint is that light bending measures how a ray deviates from a straight line in Euclidean space. In this work, we take the opposite perspective: we ask how a straight line bends in a curved space,…
In this research, we use the Gibbons-Werner method (Gauss-Bonnet theorem) on the optical geometry of a black hole and wormhole, extending the calculation of the weak gravitational lensing within the Maxwell's fish eye-like profile and dark…
A new geometric method to determine the deflection of light in the equatorial plane of the Kerr solution is presented, whose optical geometry is a surface with a Finsler metric of Randers type. Applying the Gauss-Bonnet theorem to a…
In this review, various researches on finding the bending angle of light deflected by a massive gravitating object which regard the Gauss-Bonnet theorem as the premise have been revised. Primarily, the Gibbons and Werner method is studied…
In this geometrical approach to gravitational lensing theory, we apply the Gauss-Bonnet theorem to the optical metric of a lens, modelled as a static, spherically symmetric, perfect non-relativistic fluid, in the weak deflection limit. We…
The Gibbons-Werner (GW) method is a powerful approach in studying the gravitational deflection of particles moving in curved spacetimes. The application of the Gauss-Bonnet theorem (GBT) to integral regions constructed in a two-dimensional…
Recently, we proposed a generalized Gibbons-Werner (GW) method for analyzing particle trajectories in rotating spacetimes, regardless of their asymptotic behavior [Huang \textit{et al.},…
In this letter, we have investigated the deflection angle of light by wormholes using a new geometrical method known as Gibbons-Werner method (GW). In particular we have calculated the deflection angle of light in the weak limit…
We discuss a possible extension of calculations of the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime to a non-asymptotically flat case. We examine a relation between the bending angle of light…
We apply the Gauss-Bonnet theorem to the study of light rays in a plasma medium in a static and spherically symmetric gravitational field and also to the study of timelike geodesics followed for test massive particles in a spacetime with…
In this paper, we study the weak gravitational lensing in the spacetime of rotating regular black hole geometries such as Ayon-Beato-Garc\'ia (ABG), Bardeen, and Hayward black holes. We calculate the deflection angle of light using the…
The gravitational deflection of light is a critical test of modified theories of gravity. A few years ago, Gibbons and Werner introduced a definition of the deflection angle based on the Gauss-Bonnet theorem. In more recent years, Arakida…
The Gibbons-Werner (GW) method provides a geometric framework for calculating the deflection angle of particles in curved spacetimes, and numerous extensions based on the original version have been developed in recent years to expand its…
By using the Gauss-Bonnet theorem, the bending angle of light in a static, spherically symmetric and asymptotically flat spacetime has been recently discussed, especially by taking account of the finite distance from a lens object to a…
The Gibbons-Werner-Ono-Ishihara-Asada method for gravitational lensing in a stationary spacetime has been recently reexamined [Huang and Cao, arXiv:2306.04145], in which the gravitational deflection angle of light based on the Gauss-Bonnet…
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…
In this work we extend the approach used in [Emanuel Gallo and Osvaldo M. Moreschi, Phys. Rev. D 83, 12 083007 (2011)] to the study of weak gravitational lensing in a plasma medium. First, we present expressions for the deflection angle and…
The Gibbons-Werner method for the gravitational deflection angle of unbound particles in static spherically symmetric spacetimes is based on Jacobi metric and Gauss-Bonnet theorem. When it is extended to bound massive particles, there…
In this paper we study the light bending caused by a slowly rotating source in the context of quadratic theories of gravity, in which the Einstein--Hilbert action is extended by additional terms quadratic in the curvature tensors. The…