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arXiv · 2510.21555

Gravitational and kinematic redshifts of black holes in nonlinear electrodynamics

Marco A. A. de Paula·Mustapha Azreg-Aïnou
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Abstract

Spacetimes arising from nonlinear electrodynamics (NED) are a good laboratory for studying both the nature of regular black hole (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 electrically charged, fully regular members of the h-family 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 for the gravitational and kinematic redshifts, as well as for the shadow radius, considering the effective geometry followed by photons in NED. Moreover, we consider the observational data for Sagittarius A$^{\star}$ and Messier 87$^{\star}$ BHs to impose some constraints on the charge-to-mass ratio of the fully RBHs. We obtain the general equations that govern the gravitational and kinematic redshifts of NED-sourced BH spacetimes. In particular, for fully RBHs with BH charge-to-mass ratios above some moderate value, we observe discrepancies in their physical and geometrical properties compared to those of the Reissner--Nordstr\"om (RN) BH. Therefore, our results indicate that it is possible to distinguish NED-based RBH solutions from RN BHs, from the perspective of gravitational and kinematic redshifts, suggesting potential astrophysical relevance.

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Marco A. A. de Paula, Mustapha Azreg-Aïnou. 2025-10-24. Gravitational and kinematic redshifts of black holes in nonlinear electrodynamics. https://arxiv.org/abs/2510.21555

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