Strong gravitational lensing by Kerr and Kerr-Newman black holes

TL;DR

This paper analytically investigates the strong gravitational lensing effects of Kerr and Kerr-Newman black holes, focusing on the properties of relativistic images and how black hole parameters influence their observability.

Contribution

It derives analytical formulas for light deflection near Kerr and Kerr-Newman black holes and analyzes how angular momentum and charge affect relativistic image positions and magnifications.

Findings

Angular separation and magnification of the outermost relativistic image increase with black hole spin.

Black hole charge enhances the angular separation and magnification of relativistic images.

Results suggest increased observability of relativistic images due to black hole parameters.

Abstract

We study the strong gravitational lensing due to the Kerr black holes with angular momentum $a$ and the Kerr-Newman black holes with additional charge $Q$. We first derive the analytical expressions of the deflection angles of light rays that particularly diverge as they travel near the photon sphere. In this strong deflection limit, the light rays can circle around the black hole multiple times before reaching the observer, giving relativistic images. The obtained analytical expressions are then applied to compute the angular positions and the magnifications of relativistic images due to the supermassive galactic black holes. In this work, we focus on the outermost image with reference to the optical axis. We find that its angular separation from the one closest to the optical axis and the magnification increase in angular momentum $a$ of the black holes for light rays with direct orbits. Additionally, the effects of the charge $Q$ of black holes also increase the angular separation of the outermost image from the others and the magnification for both direct and retrograde orbits. The potentially increasing observability of the relativistic images from the effects of angular momentum and charge of the black holes will be discussed.