Strong Field Gravitational Lensing by a Kerr Black Hole

TL;DR

This paper develops a new method to analyze strong gravitational lensing by Kerr black holes, including off-equatorial images, and applies it to the supermassive black hole at the Galactic center, confirming known results.

Contribution

It introduces a classification scheme for relativistic images based on photon trajectory windings and demonstrates its effectiveness in computing image positions and magnifications.

Findings

The scheme successfully computes relativistic image positions and magnifications.

Results agree with known cases in the literature.

The method applies to arbitrary source-observer geometries around Kerr black holes.

Abstract

We consider a Kerr black hole acting as a gravitational deflector within the geometrical optics, and point source approximations. The Kerr black hole gravitational lens geometry consisting of an observer and a source located far away and placed at arbitrary inclinations with respect to the black hole's equatorial plane is studied in the strong field regime. For this geometry the null geodesics equations of our interest can go around the black hole several times before reaching the observer. Such photon trajectories are written in terms of the angular positions in the observer's sky and therefore become "lens equations". As a consequence, we found for any image a simple classification scheme based in two integers numbers: the number of turning points in the polar coordinate $\theta$, and the number of windings around the black hole's rotation axis. As an application, and to make contact with the literature, we consider a supermassive Kerr black hole at the Galactic center as a gravitational deflector. In this case, we show that our proposed computational scheme works successfully by computing the positions and magnifications of the relativistic images for different source-observer geometries. In fact, it is shown that our general procedure and results for the positions and magnifications of the images off the black hole's equatorial plane, reduce and agree with well known cases found in the literature.