# Lensing, Shadow and Photon Rings in a Magnetized Black Hole Spacetime

## TL;DR

This paper studies gravitational lensing effects, including black hole shadows and photon rings, in a magnetized black hole spacetime, providing analytical formulas and methods to distinguish it from non-magnetized cases.

## Contribution

It introduces analytical formulas for shadow diameters and photon rings in a magnetized black hole spacetime, and proposes a new parameter to differentiate lensing signatures.

## Key findings

- Analytical formulas for shadow diameters at arbitrary inclination.
- Calculation of photon rings of order ≥ 2 using strong-deflection formalism.
- Introduction of the gap parameter Δ₂ to distinguish Ernst black holes from Schwarzschild black holes.

## Abstract

We analyze gravitational lensing, in particular the shadow and photon rings, in the Ernst spacetime, also known as the Schwarzschild-Melvin spacetime, which describes a Schwarzschild black hole immersed in a homogenous magnetic field. Although the geodesic equation in this spacetime is chaotic, there are some relevant features that can be determined analytically. Among other things, we give analytic formulas for the vertical diameter of the shadow for an observer at arbitrary inclination and for the horizontal diameter of the shadow for an observer in the equatorial plane. Moreover, we use the strong-deflection formalism for analytically calculating the so-called photon rings of order $\ge 2$ and we use the recently introduced gap parameter $\Delta _2$ for distinguishing lensing of an Ernst black hole from that of a Schwarzschild black hole.