Lensing by Kerr Black Holes. I: General Lens Equation and Magnification Formula

TL;DR

This paper introduces a comprehensive analytic framework for gravitational lensing by Kerr black holes, including a new lens equation and magnification formula that account for displacement effects without small angle assumptions.

Contribution

It presents the first general lens equation and magnification formula for Kerr black holes, incorporating displacement effects and applicable to asymptotically flat regions.

Findings

Derived a new lens equation for Kerr black holes.

Provided explicit displacement expressions for equatorial observers.

Validated the lens equation in spherically symmetric cases.

Abstract

We develop a unified, analytic framework for gravitational lensing by Kerr black holes. In this first paper we present a new, general lens equation and magnification formula governing lensing by a compact object. Our lens equation assumes that the source and observer are in the asymptotically flat region and does not require a small angle approximation. Furthermore, it takes into account the displacement that occurs when the light ray's tangent lines at the source and observer do not meet on the lens plane. We then explore our lens equation in the case when the compact object is a Kerr black hole. Specifically, we give an explicit expression for the displacement when the observer is in the equatorial plane of the Kerr black hole as well as for the case of spherical symmetry.