The Null Geodesics of the Kerr Exterior

TL;DR

This paper derives explicit solutions for null geodesics in Kerr spacetime by classifying potential roots and expressing integrals in elliptic form, enabling complete parametrization of light trajectories around rotating black holes.

Contribution

It provides a comprehensive, explicit parametrization of Kerr null geodesics using elliptic functions, advancing understanding of light paths in rotating black hole spacetimes.

Findings

Complete set of Kerr null geodesics expressed explicitly

Classification of potential roots for geodesic equations

Solutions in terms of Jacobi elliptic functions

Abstract

The null geodesic equation in the Kerr spacetime can be expressed as a set of integral equations involving certain potentials. We classify the roots of these potentials and express the integrals in manifestly real Legendre elliptic form. We then solve the equations using Jacobi elliptic functions, providing the complete set of null geodesics of the Kerr exterior as explicit parameterized curves.