Efficient gravitational lens optical scalars calculation of black holes with angular momentum

TL;DR

This paper introduces simplified, exact formulas for calculating gravitational lens optical scalars in Kerr spacetime, improving efficiency and accuracy, especially near black holes, by leveraging symmetries and a new observer frame concept.

Contribution

It presents novel, compact expressions for Kerr lensing calculations and a new observer frame definition, enhancing computational efficiency and accuracy over previous methods.

Findings

New compact formulas match exact calculations with high accuracy.

Efficient integration of geodesic deviation equations in Kerr geometry.

A novel observer frame concept for black hole lensing analysis.

Abstract

We provide new very simple and compact expressions for the efficient calculation of gravitational lens optical scalars for Kerr spacetime which are exact along any null geodesic. These new results are obtained recurring to well known results on geodesic motion that exploit obvious and hidden symmetries of Kerr spacetime and contrast with the rather long and cumbersome expressions previously reported in the literature, providing a helpful improvement for the sake of an efficient integration of the geodesic deviation equation on Kerr geometry. We also introduce a prescription for the observer frame which captures a new notion of \emph{center of the black hole} which can be used for any position of the observer, including those near the black hole. We compare the efficient calculation of weak lens optical scalars with the exact equations; finding an excellent agreement.