Analytic Kerr black hole lensing for equatorial observers in the strong deflection limit

TL;DR

This paper develops an analytical model for gravitational lensing by Kerr black holes in the strong deflection limit, focusing on equatorial observers, and predicts observable relativistic images near Sgr A*.

Contribution

It introduces a second-order correction to Kerr black hole lensing formulas, extending previous Schwarzschild-based models to include black hole spin effects.

Findings

Full description of caustics and lens mapping inversion for sources near caustics.

Predictions that relativistic images of Low Mass X-ray Binaries around Sgr A* could be observed.

Analytical formulas applicable to future X-ray interferometry observations.

Abstract

In this paper we present an analytical treatment of gravitational lensing by Kerr black holes in the limit of very large deflection angles, restricting to observers in the equatorial plane. We accomplish our objective starting from the Schwarzschild black hole and adding corrections up to second order in the black hole spin. This is sufficient to provide a full description of all caustics and the inversion of lens mapping for sources near them. On the basis of these formulae we argue that relativistic images of Low Mass X-ray Binaries around Sgr A* are very likely to be seen by future X-ray interferometry missions.