Effective null geodesics and black hole images in Kruglov nonlinear electrodynamics

TL;DR

This paper explores how nonlinear electrodynamics, specifically Kruglov's model, affects photon trajectories and observable black hole images, revealing significant modifications in photon orbits and shadows.

Contribution

It introduces a detailed numerical analysis of null geodesics in Kruglov nonlinear electrodynamics, highlighting observable effects on black hole imaging.

Findings

Sufficiently small positive q values create stable photon orbits outside the horizon.

Nonlinear electrodynamics significantly alters photon trajectories and black hole shadow features.

Effective geometry modifications impact relativistic images and could be observable in Sgr A* constraints.

Abstract

We investigate the effective photon geometry associated with black holes in Kruglov nonlinear electrodynamics and its consequences for strong-field optical phenomena. This model constitutes a one-parameter generalization of Born-Infeld electrodynamics, interpolating between Maxwell theory and exponential electrodynamics through the parameter $q$. For a wide range of $q$, the spacetime geometry outside the event horizon remains close to the Reissner-Nordstr\"om solution, while photon propagation is governed by an effective geometry that depends sensitively on the nonlinear electrodynamics sector. We study the corresponding null geodesic structure through fully numerical calculations, focusing on photon spheres, light deflection, black hole shadows, and accretion-disk images. The effective geometry shows qualitatively distinct features depending on $q$. In particular, sufficiently small positive values of $q$ generate stable photon orbits outside the event horizon, together with significant modifications to the range of impact parameters supporting multiple photon trajectories. These effects produce observable modifications in the relativistic images, including systematic variations in the effective geometry. We also analyze the black hole shadow in relation to current horizon-scale constraints on Sgr~A*. Our results demonstrate that nonlinear electrodynamics can substantially modify photon propagation and relativistic image formation even when the underlying spacetime gometry remains close to the Maxwell electrodynamics case.