Wavefronts, Caustic Sheets, and Caustic Surfing in Gravitational Lensing

This work reviews the basic theoretical aspects, the main observational evidences and the recent applications of gravitational lensing in the Universe. The article is aimed particularly at providing the readers who don't work on gravitational lensing a relatively easy introduction to this active research field in today's astrophysics.

Wave effects in lensing form a rich phenomenon at the intersection of classical caustic singularities and quantum interference, yet are notoriously difficult to model. A large number of recently observed pulsars and fast radio bursts in radio astronomy and the prospected increase in sensitivity of gravitational wave detectors suggest that wave effects will likely be observed in the near future. The interference fringes are sensitive to physical parameters which cannot be infe...

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 calculations and applied to multiple quasar system of PG1115+080. Consistencies with elliptical lens models are also discussed.

We revisit the gravitational lensing phenomenon using a new visualization technique. It consists in projecting the observers sky into the source plane, what gives rise to a folded and stretched surface. This provides a clear graphical tool to visualize some interesting well-known effects, such as the development of multiple images of a source, the structure of the caustic curves, the parity of the images and their magnification as a function of the source position.

We investigate the caustic topologies for binary gravitational lenses made up of two objects whose gravitational potential declines as $1/r^n$. With $n<1$ this corresponds to power-law dust distributions like the singular isothermal sphere. The $n>1$ regime can be obtained with some violations of the energy conditions, one famous example being the Ellis wormhole. Gravitational lensing provides a natural arena to distinguish and identify such exotic objects in our Universe. We...

The gravitational field of supermassive black holes is able to strongly bend light rays emitted by nearby sources. When the deflection angle exceeds $\pi$, gravitational lensing can be analytically approximated by the so-called strong deflection limit. In this paper we remove the conventional assumption of sources very far from the black hole, considering the distance of the source as an additional parameter in the lensing problem to be treated exactly. We find expressions fo...

Despite its mathematical complexity, the multiple gravitational lens can be studied in detail in every situation where a perturbative approach is possible. In this paper, we examine the caustics of a system with a lens very far from the others with respect to their Einstein radii, and a system where mutual distances between lenses are small compared to the Einstein radius of the total mass. Finally we review the case of a planetary system adding some new information (area of ...

There are compelling reasons to believe that the dark matter of the universe is constituted, in large part, by non-baryonic collisionless particles with very small primordial velocity dispersion. Such particles are called cold dark matter (CDM). The leading candidates are axions and weakly interacting massive particles (WIMPs). The word ``collisionless'' indicates that the particles are so weakly interacting that they move purely under the influence of gravity. Galaxies are s...

We investigate the possibility of determining the mass distribution of a gravitational lens via lensing observations. We consider an extended, compact gravitational lens, representing its static external gravitational potential via an infinite set of symmetric trace free (STF) multipole moments. Within the wave-optical treatment, we evaluate the caustics formed in the lens's point spread function (PSF). We study the only quantity that is available in astronomical lensing obse...

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 outside, on, and inside the cusped caustic. We obtain results on how the image magnifications scale with respect to separation from the cusped caustic for arbitrary source positions. Along the axis of symmetry of the cusp, the total magnificatio...