Gravitational lensing by massive and exotic objects

Gravitational lensing is an important tool in astrophysics and in cosmology widely used to study both populations of compact objects (including exoplanets, black holes and other stellar remnants), and extended objects, such as galaxies, clusters of galaxies and large-scale structures. Since most of the mysteries of our Universe do not show up in observations based on electromagnetic interactions, gravitational lensing is more and more employed to study the dark side of the Universe, including dark matter, dark energy, and any kind of exotic matter (such as wormholes) conjectured by theorists. In this presentation we run across the history of gravitational lensing through the explanation of the lens equation, the magnification of images, the description of critical curves and caustics, the binary lenses in the standard theory, then we focus on gravitational lensing by objects with 1/rn potential giving a complete atlas of the critical curves and caustics in mixed binary systems such as pairs of galaxies with different halos, or cases in which one object is made up of exotic matter and the other one is a normal star or in the case of wormholes when they appear in non-isolated systems. After the amazing discoveries by the GRAVITY collaboration in thelast few years on the star S2 orbiting the black hole Sgr A* in the center of the Milky Way, we present a detailed investigation of the impact of gravitational lensing on the reconstruction of stellar orbits around this massive black hole.