Related papers: The Fermat Principle in General Relativity and App…
We present a simplified version of the lowest-order embedded point mass gravitational lens theory and then make the extension of this theory to any embedded transparent lens. Embedding a lens effectively reduces the gravitational…
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…
Fermat's principle is fully generalized to the case where a smooth interface separates two cone structures -- Lorentz-Finsler lightcones -- representing wave propagation in a potentially inhomogeneous, anisotropic, time-dependent and…
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…
Building on the results of previous work, we demonstrate how matter fields are incorporated into the general linear frame approach to general relativity. When considering the Maxwell one-form field, we find that the system that leads…
Even when used to describe the same phenomenon, equations, graphics and words each give different perspectives and lead to complementary insights. The basic elements of strong gravitational lensing are introduced here favoring words and…
Using the linearized theory of general relativity, the gravitomagnetic analogue of the Barnett effect is derived. Further theoretical and experimental investigation is recommended, due to the expected macroscopic values of the…
We analyzed the influence of static gravitational field on the vacuum and proposed the concept of inhomogeneous vacuum. According to the corresponding Fermat's principle in the general relativity, we derived a graded refractive index 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…
The theory of gravitational lensing has revealed many generic and fundamental properties of compact objects like black holes and wormholes. In this article, we utilize a recent formulation to compute the quantum effects on the deflection…
Interactions incorporating the vacuum polarization effects in curved backgrounds modify the null cone structure in such a way that the photon trajectories would not be the space-time geodesics anymore. The gravitational birefringence…
The present work shows that through a suitable change of variables relativistic dynamics can be mapped to light propagation in a non-homogeneous medium. A particle's trajectory through the modified space-time is thus formally equivalent to…
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…
The contribution of the cosmological constant to the deflection angle and the time delays are derived from the integration of the gravitational potential as well as from Fermat's Principle. The findings are in agreement with recent results…
This study aims to investigate the strong gravitational lensing effects in $f(T)$ gravity. We present the theoretical analytic expressions for the lensing effects in $f(T)$ gravity, including deflection angle, magnification, and time delay.…
In this paper we investigate a complex symmetric generalization of general relativity and in particular we investigate its linearized field equations. We begin by reviewing some basic definitions and structures in Moffat's symmetric complex…
Fermat's principle applied to a flat metric in the plane yields the phase of a Bessel function in the periodic domain for a constant index of refraction. Gravitational forces cause the index of refraction to vary and lead to a modified…
We describe local light-ray rotation in terms of complex refractive indices. We show that Fermat's principle holds, and we derive an extended Snell's law. The change in the angle of a light ray with respect to the normal to a…
Linearized general relativity admits a formulation in terms of gravitoelectric and gravitomagnetic fields that closely parallels the description of the electromagnetic field by Maxwell's equations. For steady mass currents, this formalism…
In general relativity the fermions are treated from the perspective of the gauged Lorentz group and by introducing the corresponding gauge fields the spin connection. This procedure is intimately related to the so-called "vielbein"…