This analysis reveals the features of gravitational lensing and photon rings in an Ernst black hole, suggesting distinct characteristics compared to traditional black holes.
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 ≥ 2 and we use the recently introduced gap parameter Δ₂ for distinguishing lensing of an Ernst black hole from that of a Schwarzschild black hole.
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Khan et al. (2025) studied this question.
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