Regular Magnetically Charged Black Holes from Nonlinear Electrodynamics: Thermodynamics, Light Deflection, and Orbital Dynamics

Abstract: We investigate the thermodynamic properties, light deflection, and orbital dynamics of regular magnetically charged black holes (NRCBHs) arising from nonlinear electrodynamics (NED) coupled to general relativity. The metric function $f(r)$ ensures complete regularity at the origin while maintaining asymptotic flatness, with the extremal magnetic charge limit reaching $q_{\text{ext}} \approx 2.54M$, significantly exceeding the Reissner-Nordstr\"{o}m value. Using the quantum tunneling framework, we derive the Hawking temperature and incorporate generalized uncertainty principle (GUP) corrections, showing $T_{\text{GUP}} = (f'(r_h)/4\pi)\sqrt{1-2\beta m_p^2}$. The weak deflection of light is analyzed through the Gauss-Bonnet theorem (GBT), revealing charge-dependent behavior where large $q$ values lead to negative deflection angles due to electromagnetic repulsion. Plasma effects further modify the deflection through the refractive index $n(r) = \sqrt{1 - \omega_p^2(r)f(r)/\omega_0^2}$. Keplerian motion analysis demonstrates that the angular velocity $\Omega(r)$ exhibits charge-sensitive maxima related to quasi-periodic oscillations (QPOs) in accretion disks. Finally, we examine Joule-Thomson expansion (JTE) properties, finding that the coefficient $\mu_J$ indicates cooling behavior for higher charges and larger event horizons. Our results provide comprehensive insights into the observational signatures of NRCBHs, with implications for gravitational lensing, X-ray astronomy, and tests of nonlinear electromagnetic theories in strong gravitational fields.