BiGONLight: a new package for computing optical observables in Numerical Relativity

Abstract

The investigation of relativistic effects in the most general way requires a unified treatment of light propagation in cosmology. This goal can be achieved with the new interpretation of the geodesic deviation equation in terms of the bilocal geodesic operators (BGO). The BGO formalism extends the standard formulation, providing a unified framework to describe all possible optical phenomena due to the interaction between light and spacetime curvature. In my dissertation, I present {\tt BiGONLight}, a {\tt Mathematica} package that applies the BGO formalism to study light propagation in numerical relativity. The package encodes the 3+1 bilocal geodesic operators framework as a collection of {\tt Mathematica} functions. The inputs are the spacetime metric plus the kinematics of the observer and the source in the form of the 3+1 quantities, which may come directly from a numerical simulation or can be provided by the user as analytical components. These data are then used for ray tracing and computing the BGOs in a completely general way, i.e. without relying on symmetries or specific coordinate choices. The primary purpose of the package is the computation of optical observables in arbitrary spacetimes. The uniform theoretical framework of the BGO formalism allows for the extraction of multiple observables within a single computation, while the {\tt Wolfram} language provides a flexible computational framework that makes the package highly adaptable to perform both numerical and analytical studies of light propagation.