A review on analytical studies in gravitational lensing

Abstract

In this study, we review some current studies on gravitational lensing for black holes, mainly in the context of general relativity. We mainly focus on the analytical studies related to lensing with references to observational results. We start with reviewing lensing in spherically symmetric Schwarzschild spacetime, showing how to calculate deflection angles before moving to the rotating counterpart, the Kerr metric. Furthermore, we extend our studies for a particular class of newly proposed solutions called black-bounce spacetimes and discuss throughout the review how to explore lensing in these spacetimes and how the various parameters can be constrained using available astrophysical and cosmological data.