PyGRO: A Python integrator for General Relativistic Orbits

Departamento de Física Fundamental y Matemáticas, Universidad de Salamanca, Patio de Escuelas 1, Salamanca 37008, Spain

^★ Corresponding author: rdellamonica@usal.es

Received: 27 February 2025
Accepted: 25 April 2025

Abstract

The advancement in recent years in the field of experimental gravitation has allowed for testing of the equivalence principle in regimes that were previously unexplored and for unprecedented verifications of general relativity while also enabling tests of alternative theories of gravity. We introduce a new computational tool, PyGRO, with the aim of numerically integrating the geodesic equations for the trajectories of massive and massless test particles in any analytic four-dimensional space-time. The result of our work is a fast, modern, highly customizable, and user-friendly open-source Python package that can perform numerical integration of the geodesic equations. Combining symbolic and numerical calculations, PyGRO offers a variety of methods to obtain fully relativistic orbits with minimal intervention by the user, and it is able to work in full generality with any user-given symbolic expression of the space-time metric tensor. We tested PyGRO in an array of scenarios, and we validated the methodology by successfully reproducing classical results from general relativity, which we report in this article.