Geometric optics in static spherically symmetric spacetimes

Studying the geometry of the Universe through the observation of light is a long-standing problem. Although in general the propagation of light satisfies Maxwell equations, in practice it is often sufficient to work within a much simpler framework of geometric optics for whom a solid foundation was laid almost six decades ago. However, this formalism is incomplete in the sense that it cannot accommodate parallax effects or cumulative changes of observables in time. In my talk, I will present the bilocal geodesic operator formalism whereby the solution of the linear geodesic deviation equation can describe all these effects and provide a way to disentangle special and general relativistic contributions. In the second part of my talk, I will briefly describe two methods of solving the linear geodesic deviation equation exactly and apply them to the static spherically symmetric spacetimes. Finally, I will discuss the behaviour of angular diameter and parallax distances as well as the emitter-observer independent distance slip in the Schwarzschild spacetime.