FANTASY: User-Friendly Symplectic Geodesic Integrator for Arbitrary Metrics with Automatic Differentiation

TL;DR

FANTASY is an easy-to-use, open-source symplectic geodesic integrator in Python that automatically computes derivatives and handles arbitrary metrics without manual input of Christoffel symbols.

Contribution

It introduces a user-friendly, automatic differentiation-based integrator that works with arbitrary metrics and includes automatic coordinate transformations.

Findings

Efficiently computes derivatives with machine precision

Supports arbitrary metrics without manual Christoffel symbols

Includes prebuilt second and fourth order schemes

Abstract

We present FANTASY (Finally A Numerical Trajectory Algorithm both Straightforward and sYmplectic), a user-friendly, open-source symplectic geodesic integrator written in Python. FANTASY is designed to work "out-of-the-box" and does not require anything from the user aside from the metric and the initial conditions for the geodesics. FANTASY efficiently computes derivatives up to machine precision using automatic differentiation, allowing the integration of geodesics in arbitrary space(times) without the need for the user to manually input Christoffel symbols or any other metric derivatives. Further, FANTASY utilizes a Hamiltonian integration scheme that doubles the phase space, where two copies of the particle phase space are evolved together. This technique allows for an integration scheme that is both explicit and symplectic, even when the Hamiltonian is not separable. FANTASY comes prebuilt with second and fourth order schemes, and is easily extendible to higher order schemes. FANTASY also includes an automatic Jacobian calculator that allows for coordinate transformations to be done automatically.