A Fast New Public Code for Computing Photon Orbits in a Kerr Spacetime

TL;DR

This paper introduces a new, efficient method for calculating photon trajectories in Kerr spacetime, simplifying computations and providing a publicly available code for astrophysical applications.

Contribution

A novel semi-analytical technique reduces the equations of motion to elliptic integrals, enabling rapid and accurate photon orbit calculations in Kerr spacetime.

Findings

Method achieves faster computation times.

Code is publicly available for community use.

Accurate photon trajectory calculations demonstrated.

Abstract

Relativistic radiative transfer problems require the calculation of photon trajectories in curved spacetime. We present a novel technique for rapid and accurate calculation of null geodesics in the Kerr metric. The equations of motion from the Hamilton-Jacobi equation are reduced directly to Carlson's elliptic integrals, simplifying algebraic manipulations and allowing all coordinates to be computed semi-analytically for the first time. We discuss the method, its implementation in a freely available FORTRAN code, and its application to toy problems from the literature.