Horizon, Null-Orbit, and Photon-Sphere Phase Structures in Logarithmic Nonlinear Electrodynamics

Peshwaz Abdulkareem Abdoul

paper

Horizon, Null-Orbit, and Photon-Sphere Phase Structures in Logarithmic Nonlinear Electrodynamics

arXiv:2609.34957

Abstract

We investigate static, charged, asymptotically flat black holes in logarithmic nonlinear electrodynamics (LNED) within the $(Q, ε)$ parameter space. We distinguish three phase structures: the horizon geometry, the background circular null orbits, and the circular photon orbits of the effective optical geometry. All share a zero-radius boundary $Q_{n c} (ε; M) = γ M^{2/3} ε^{1/6}$ , but possess distinct critical structures: the extremal curve $Q_{e x t} (ε; M)$ and the background merger curve $Q_{m} (ε; M)$ both terminate at the bifurcation point $(Q_{b}, ε_{b})$ , located at $r = 0$ . In contrast, the effective photon-orbit merger curve $Q_{m}^{p h} (ε; M)$ does not pass through this point. For $ε \geq ε_{b}$ , approaching $Q_{n c}$ shrinks the horizon to zero radius, resulting in black points with non-zero, quantum-corrected entropy. Their Hawking temperature vanishes at the bifurcation point and diverges for $ε > ε_{b}$ , except when $η δ = 1$ , where the temperature at the bifurcation point also diverges. The background potential $V_{e f f}^{b g} (r)$ develops an infinite barrier at $r = 0$ without local extrema, acting as a perfect repeller. In contrast, the photon potential $V_{e f f}^{p h} (r)$ is regularized with a maximum at a finite radius, acting as a partial reflector. Consequently, the black points retain photon spheres of finite radius. Away from $Q_{n c}$ , for $ε < ε_{b}$ , both geometries support horizonless structures above $Q_{e x t}$ ; for $ε \geq ε_{b}$ , only the optical geometry does so in the region $Q_{n c} < Q < Q_{m}^{p h}$ . Non-radial geodesics are blocked from the singularity and can form metastable bound states, while radial geodesics either reach $r = 0$ or escape to infinity. The critical impact parameter encodes both gravitational and optical-geometry effects, probing the distinct phase structures.

arXiv comment36 pages, 8 figures