Lensing of electromagnetic and gravitational waves

This project explores how light and gravitational waves travel through the universe, in particular when their paths are distorted by the gravitational field of massive cosmic objects such as black holes or galaxies. An effect known as gravitational lensing can magnify, shift, or even duplicate the images of distant sources. This offers astronomers powerful tools to observe faraway objects and to study how gravity operates in extreme conditions. While gravitational lensing is a well-established phenomenon, most models assume that the sources and lenses do not move and that waves behave like simple rays of light. This project challenges those assumptions by investigating what happens when we account for motion, wave effects, and the strong gravitational fields found near black holes. One aim is to understand how the apparent position and color (redshift) of a distant light source changes over time due to lensing by moving objects. These small shifts, normally too subtle to be detected, may become greatly amplified when a source lies near a caustica region where the lensing effect is particularly strong. By modeling these effects and estimating their size under realistic conditions, this project will assess whether future observations could use them to detect sideways motion in faraway cosmic sources. This could offer a new way to measure the movement of distant galaxies or quasars, deepening our understanding of the structure and evolution of the universe. At the same time, the project investigates how gravitational wavesripples in spacetime created by violent cosmic eventsare affected by strong gravitational lensing. In particular, we focus on systems where two black holes merge while orbiting a much larger black hole. These so-called hierarchical systems create complex wave signals that are bent and modified as they pass near the massive object. By simulating how these waves are distorted, the project aims to predict how such signals would look like to gravitational wave detectors on Earth. This may help astronomers recognize such systems in real data and learn more about the environments in which black holes grow and merge. To fully capture the behavior of waves in such extreme settings, the project will also develop a new mathematical approach that goes beyond traditional ray-based models. Inspired by techniques from quantum physics, this approach uses a tool called the Wigner function to describe how waves evolve when interference and diffraction become importantparticularly near caustics, where previous models break down. Applying this framework to curved spacetime will make it possible to study wave effects that were previously out of reach and may lead to more accurate predictions in a wide range of astrophysical situations. Together, these efforts aim to expand the tools available to modern astrophysics, offering a more complete picture of how light and gravity interact across vast cosmic distances and under extreme physical conditions.