相关论文: Geometry of Universal Magnification Invariants

We review five often used quad lens models, each of which has analytical solutions and can produce four images at most. Each lens model has two parameters, including one that describes the intensity of non-dimensional mass density, and the…

We reconsider the phenomenon of mass generation via coordinate-dependent compatifications of higher-dimensional theories on orbifolds. For definiteness, we study a generic five-dimensional (5D) theory compactified on S^1/Z_2. We show that…

We present a rigorous, detailed study of the generic, quantitative properties of gravitational microlensing near cusp catastrophes. We derive explicit formulas for the total magnification and centroid of the images created for sources…

According to the theory of general relativity, masses deflect light in a way similar to convex glass lenses. This gravitational lensing effect is astigmatic, giving rise to image distortions. These distortions allow to quantify cosmic…

Gravitational lensing magnification is maximal around caustics. At these source locations, an incoming wave from a point source would formally experience an infinite amplification in the high-frequency or geometric optics limit. This…

Singularities of caustics appeared in gravitational lensing effect are discussed analytically. Multipole expansion model of lensing object is mainly studied since it is tractable and universal. Our analyses are confirmed by numerical…

The standard definition of gravitational lensing magnification is generalized to Lorentzian spacetimes, and it is shown how it can be interpreted geometrically in terms of the van Vleck determinant and the exponential map. This is joint…

We obtain new general results on the structure of the space of translation invariant continuous valuations on convex sets (a version of the hard Lefschetz theorem). Using these and our previous results we obtain explicit characterization of…

We study the local behavior of gravitational lensing near fold catastrophes. Using a generic form for the lensing map near a fold, we determine the observable properties of the lensed images, focusing on the case when the individual images…

The multiple images of lensed quasars provide evidence on the mass distribution of the lensing galaxy. The lensing invariants are constructed from the positions of the images, their parities and their fluxes. They depend only on the…

We define compactness of a gravitational lens as the scaled closest distance of approach (i.e., $r_0/M$) of the null geodesic giving rise to an image. We model forty supermassive dark objects as Schwarzschild lenses and compute compactness…

We are developing a general, unified, and rigorous analytical framework for using gravitational lensing by compact objects to test different theories of gravity beyond the weak-deflection limit. In this paper we present the formalism for…

The observables in a strong gravitational lens are usually just the image positions and sometimes the flux ratios. We develop a new and simple algorithm which allows a set of models to be fitted exactly to the observations. Taking our cue…

When gravitational waves propagate near massive objects, their paths curve resulting in gravitational lensing, which is expected to be a promising new instrument in astrophysics. If the time delay between different paths is comparable with…

For spacelike stationary (i.e. zero mean curvature) surfaces in 4-dimensional Lorentz space one can naturally introduce two Gauss maps and Weierstrass representation. In this paper we investigate their global geometry systematically. The…

We introduce the universal functorial equivariant Lefschetz invariant for endomorphisms of finite proper G-CW-complexes, where G is a discrete group. We use K_0 of the category of "phi-endomorphisms of finitely generated free…

We discuss the classic theorem according to which a gravitational lens always produces a total magnification greater than unity. This theorem seems to contradict the conservation of total flux from a lensed source. The standard solution to…

We pursue a geometrical approach to gravitational lensing theory. We present a survey of the background theory of General Relativity, including particular properties of the Schwarzschild and Kerr solutions. Next we outline a proof of the…

After a short summary of our bimetric model of the Universe, an exact nonlinear solution is built, which demonstrates the existence of solutions for our two coupled field equations system. In addition to the classical positive gravitational…

Symplectic four-manifolds give rise to Lefschetz fibrations, which are determined by monodromy representations of free groups in mapping class groups. We study the topology of Lefschetz fibrations by analysing the action of the monodromy on…