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We relate the observable number of sources per solid angle and redshift to the underlying proper source density and velocity, background evolution and line-of-sight potentials. We give an exact result in the case of linearized perturbations…
The paper contains the inversion formula for the weighted spherical mean. The interest to reconstruction a function by its integral by sphere grews tremendously in the last six decades, stimulated by the spectrum of new problems and methods…
Microlensing imprints by typical stellar mass lenses on gravitational waves are challenging to identify in the LIGO and Virgo frequency band because such effects are weak. However, stellar mass lenses are generally embedded in lens galaxies…
We present a new perspective on gravitational lensing. We describe a new extension of the weak lensing formalism capable of describing strongly lensed images. By integrating the non-linear geodesic deviation equation, the amplification…
The basic concepts of gravitational microlensing are introduced. We start with the lens equation, and then derive the image positions and magnifications. The statistical quantities of optical depth and event rate are then described. We…
Gravitational lensing in metric theories of gravity is discussed. I introduce a generalized approximate metric element, inclusive of both post-post-Newtonian (ppN) contributions and gravito-magnetic field. Following Fermat's principle 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…
Strong gravitational lensing provides a wealth of astrophysical information on the baryonic and dark matter content of galaxies. It also serves as a valuable cosmological probe by allowing us to measure the Hubble constant independently of…
Weak gravitational lensing has several important effects on the cosmic microwave background (CMB): it changes the CMB power spectra, induces non-Gaussianities, and generates a B-mode polarization signal that is an important source of…
We study the morphology of convergence maps by perturbatively reconstructing their Minkowski Functionals (MFs). We present a systematics study using a set of three generalised skew-spectra as a function of source redshift and smoothing…
Strong gravitational lensing has significantly advanced the study of high-redshift galaxies, but the differential magnification effect inevitably introduces biases in the spectral analysis of source galaxies. This work investigates these…
In this article we review the astrophysical application of gravitational microlensing. After introducing the history of gravitational lensing, we present the key equations and concept of microlensing. The most frequent microlensing events…
We report a significant detection of weak, tangential distortion of the images of cosmologically distant, faint galaxies due to gravitational lensing by foreground galaxies. A mean image polarisation of $<p>=0.011\pm 0.006$ is measured for…
Perfect lensing using negative refractive index materials and radiationless electromagnetic interference both provide extreme subwavelength focusing by "amplifying" evanescent wave components that are usually lost. This paper provides a…
In a previous paper, we outlined a new Bayesian method for inferring the properties of extended gravitational lenses, given data in the form of resolved images. This method holds the most promise for optimally extracting information from…
Gravitational waves (GWs) from distant sources such as inspiralling and merging stellar-mass compact binaries, intermediate-mass and supermassive-binary-black-hole can be gravitationally lensed by intervening objects, ranging from stars and…
The effect of currents of mass on bending of light rays is considered in the weak field regime. Following Fermat's principle and the standard theory of gravitational lensing, we derive the gravitomagnetic correction to time delay function…
With the increase in the number of observed gravitational wave (GW) signals, detecting strongly lensed GWs by galaxies has become a real possibility. Lens galaxies also contain microlenses (e.g., stars and black holes), introducing further…
We consider microlensing of an elliptical source crossing a fold caustic. We derive a simple expression for the light curve of a source with uniform surface brightness that is accurate to third order in the ellipticity e (yielding errors of…
Free electrons moving in an optical standing wave field feel the ponderomotive potential, acting as a refractive-index medium in electron optics. Emerging technologies involving this potential have been proposed and realized in electron…