Rotating gravitational lenses: a kinematic approach

TL;DR

This paper derives a kinematic approach to rotating gravitational lenses using Kerr geodesic equations, enabling efficient modeling of light paths and caustic patterns around rotating masses.

Contribution

It introduces a novel kinematic method based on Kerr geodesics for analyzing light deflection and caustics in rotating gravitational fields.

Findings

Derived acceleration vectors in Boyer-Lindquist and Cartesian coordinates.

Produced caustic pattern plots for a rotating mass system.

Developed first and second order approximations for light paths.

Abstract

This paper uses the Kerr geodesic equations for massless particles to derive an acceleration vector in both Boyer-Lindquist and Cartesian coordinates. As a special case, the Schwarzschild acceleration due to a non-rotating mass has a particularly simple and elegant form in Cartesian coordinates. Using forward integration, these equations are used to plot the caustic pattern due to a system consisting of a rotating point mass with a smaller non-rotating planet. Additionally, first and second order approximations to the paths are identified, which allows for fast approximations of paths, deflection angles and travel-time delays.