Exploring potential astrophysical applications of black holes in nonlinear electrodynamics

TL;DR

The paper addresses how electrically charged regular black holes from nonlinear electrodynamics (NED) within general relativity imprint observable signatures on photon propagation. It analyzes two fully RBHs from the h-family ($h=0,2$) in the F framework, deriving photon motion in the NED-induced effective geometry, a shadow formula for static observers, and the weak deflection angle via the Gauss-Bonnet theorem, while also deriving a general redshift expression that separates gravitational and kinematic components. The main findings show that, for moderate charge-to-mass ratios, the shadows and weak-field lensing closely resemble Reissner–Nordström, but increasingly diverge at higher charges, with Sgr A$^{*}$ disfavoring extremely charged cases (especially for $h=2$ at 2σ) and M87$^{*}$ allowing them at 2σ; kinematic redshifts near the smallest circular geodesics offer a more pronounced distinction between NED RBHs and RN. Overall, the work highlights the potential astrophysical relevance of NED RBHs as probes of strong-field electrodynamics and provides a framework for applying shadow and redshift observables to constrain NED parameters in real black holes.

Abstract

Spacetimes arising from nonlinear electrodynamics (NED) are a good laboratory for studying both the nature of regular black holes (RBH) solutions and the imprints of nonlinear electromagnetic fields within this context. Over the past few decades, NED-sourced black hole (BH) spacetimes have attracted considerable attention, but electrically charged RBHs obtained in the so-called $F$ framework have been less addressed in the literature. We consider two members of the h-family of electrically charged, fully RBHs that are solutions to general relativity minimally coupled to NED. Because of their potential astrophysical and astronomical applications, we mainly focus our investigation on the motion of photons and its implications in the shadow radius and gravitational and kinematic redshift, considering the effective geometry followed by photons in NED. For a BH charge-to-mass ratio below some moderate value, there is almost no way to distinguish these members (and likely all members) of the h-family from the Reissner-Nordström (RN) BH. In its turn, for a BH charge-to-mass ratio above some moderate value, we observe discrepancies in their physical and geometric properties in comparison to those of the RN BH. Furthermore, we also consider observational data for Sagittarius A$^{*}$ and Messier 87$^{*}$ BHs to impose some constraints on the charge-to-mass ratio of the fully RBHs.

Figures (10)

• Figure 1: Metric function \ref{['n84a']}, for distinct values of $q$, as a function of $r/M$.
• Figure 2: KS of the spacetime given by the metric function \ref{['n84a']}, considering different choices of $q$, as a function of $r/M$.
• Figure 3: Metric function \ref{['n84a2']}, for distinct values of $q$, as a function of $r/M$.
• Figure 4: KS of the spacetime given by the metric function \ref{['n84a2']}, considering different choices of $q$, as a function of $r/M$.
• Figure 5: Ratio between the shadow radius of the fully RBH with $h = 2$, as a function of $q$, for two distinct scenarios: (i) considering the effective $\bar{r}_{\text{s}}$ and standard $r_{\text{s}}$ geometries (top panel); and (ii) considering $\bar{r}_{\text{s}}$ and the shadow radius of the RN case, denoted by $r_{\text{s}}^{\text{RN}}$ (bottom panel).