Dynamics of Geodesics in Non-linear Electrodynamics Corrected Black Hole and Shadows of its Rotating Analogue

TL;DR

This work analyzes how nonlinear electrodynamics (NLED) corrections modify particle motion and light propagation around a Schwarzschild-like black hole and its rotating analogue. By deriving geodesic equations and applying backward ray-tracing, it shows that the photon-sphere radius $r_{ph}$ grows with the NLED coupling $\zeta$ and magnetic charge $Q$, and that timelike orbits experience a deeper effective potential and inward ISCO with stronger nonlinearity. Extending to rotation via a modified Newman–Janis algorithm, the study characterizes the ergoregion and shadows, finding that spin $a$ flattens the shadow while NLED effects (higher $\zeta$) can offset some frame-dragging, and larger $Q$ enlarges the shadow. These results highlight the potential of shadow and lensing observations to constrain NLED parameters and probe gravito-electromagnetic couplings in strong-field regimes.

Abstract

We study the nature of particle geodesics around a non-linear electrodynamic black hole (NLED-BH) inspired by the confinement of a heavy quark-antiquark system, which reduces to Maxwell's linear electrodynamics theory at the strong field regime. The corrected BH solution is a special generalisation of the Schwarzschild BH at the linear regime. Such a type of corrected system is parameterised by a charge parameter along with a non-linear electrodynamic term $ζ$. To be specific, we studied the geodesic behaviour of massless null particles through the geodesic equations using the backward ray-tracing method. We also investigated how NLED effects in charged BH spacetimes affect timelike particle orbits, specifically properties like precession frequency and orbital velocity around the NLED BH. Furthermore, to extend the analysis to the rotating case, we used the modified Newman-Janis algorithm to generate the rotating analogue of the NLED BH. We then analysed the ergosphere formation and shadow cast by the rotating analogue of the NLED BH.

Figures (10)

• Figure 1: The lapse function is shown with respect to different values of $\zeta$ and $Q$
• Figure 2: The null trajectories obtained through the backward ray-tracing around the NLED BH are shown for different values of $\zeta$.
• Figure 3: The null trajectories obtained through the backward ray-tracing around the NLED BH are shown for different values of $Q$.
• Figure 4: The effective potential for timelike particles is shown. Here we have set $M = 1$ and $L = 5$.
• Figure 5: The geodesic precession frequency is shown for different values of the NLED parameter $\zeta$ and charge $Q$