Optical and orbital characterization of spherically symmetric static black holes of self-gravitating new nonlinear electrodynamics model

Abstract

Horizon scale imaging and precision lensing have turned black holes into quantitative laboratories for strong gravity and for non standard electromagnetic physics. We study the optical appearance and orbital dynamics of a new class of static spherically symmetric black holes sourced by a Palatini inspired nonlinear electrodynamics model, minimally coupled to Einstein-Hilbert gravity. Using a unified geodesic analysis, we identify the key radii that organize the strong field phenomenology. For photons we determine the unstable photon sphere, the associated critical capture threshold, and the resulting shadow size for a distant observer, and we map how these observables respond to the charge and to the nonlinearity index $n$. For massive probes we compute circular orbits and the innermost stable circular orbit, clarifying the departure from the Schwarzschild and Reissner-Nordström cases. We then connect to classical tests by evaluating the light deflection angle and periastron advance, providing additional diagnostics that complement the shadow. Our results furnish a practical reference model for confronting first order nonlinear electrodynamics black holes with current and forthcoming imaging and lensing data.

Figures (14)

• Figure 1: Lapse function $f(\rho)$ of BH solutions of the PINLED $Y^n$ model with various values of $q$ for $n$ values $n=2,3 , 4$ with $m_{BH}=3$.
• Figure 2: Horizon radius $\rho_H$ versus black hole mass $m_{BH}$ for $Y^n$ BHs with various values of $q$ for $n= 2,3 , 4$. Notice that $q=4.40353$ is the critical $q$ for $m_{BH}=3$ and $n=2$, which corresponds to a naked singularity for $n=3$ and $4$.
• Figure 3: Effective potential for massive particles ($\xi=1$) vs radius $\rho$ for $Y^n$ BHs with various values of $q$ for $n$ values 2,3 and 4 with $m_{BH}=3$ and $L=4 m_{BH}$. Notice that the next to largest zero of $V_{\text{eff}}(\rho)$ is at the event horizon, and that the minimum of $V_{\text{eff}}(\rho)$ which is relevant to the circular orbits and ISCO is the shallow one further to the right around $\rho=40$ in these plots.
• Figure 4: ISCO radius for massive particles ($\xi = 1$) as a function of the BH mass $m_{\rm BH}$ for the $Y^n$ BHs, shown for various values of the charge $q$ and for $n = 2, 3,$ and $4$. In the inset panel, dashed curve correspond to the Reissner–Nordström (RN) case. For $n = 3$ and $4$, the difference between the PINLED and RN results becomes indistinguishable even in smaller scales.
• Figure 5: ISCO radius for massive particles ($\xi=1$) as a function of the charge $q$ for the $Y^n$ BHs with various fixed values of the BH mass $m_{\rm BH}$ and for $n=2,3,$ and $4$. In the inset panel the dashed curve represent the corresponding RN results.