Horizon, Null-Orbit, and Photon-Sphere Phase Structures in Logarithmic Nonlinear Electrodynamics
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 Qnc(ε;M)=γM2/3ε1/6, but possess distinct critical structures: the extremal curve Qext(ε;M) and the background merger curve Qm(ε;M) both terminate at the bifurcation point (Qb,εb), located at r=0. In contrast, the effective photon-orbit merger curve Qmph(ε;M) does not pass through this point. For ε≥εb, approaching Qnc 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>εb, except when ηδ=1, where the temperature at the bifurcation point also diverges. The background potential Veffbg(r) develops an infinite barrier at r=0 without local extrema, acting as a perfect repeller. In contrast, the photon potential Veffph(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 Qnc, for ε<εb, both geometries support horizonless structures above Qext; for ε≥εb, only the optical geometry does so in the region Qnc<Q<Qmph. 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.
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BibTeX
@misc{abdoul2026horizon,
title = {{Horizon, Null-Orbit, and Photon-Sphere Phase Structures in Logarithmic Nonlinear Electrodynamics}},
author = {Peshwaz Abdulkareem Abdoul},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.34957},
eprint = {2609.34957},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34957},
}
RIS
TY - UNPB
TI - Horizon, Null-Orbit, and Photon-Sphere Phase Structures in Logarithmic Nonlinear Electrodynamics
AU - Peshwaz Abdulkareem Abdoul
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2609.34957
UR - https://arxiv.org/abs/2609.34957
AB - 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_nc(ε;M)=γM^2/3ε^1/6, but possess distinct critical structures: the extremal curve Q_ext(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^ph(ε;M) does not pass through this point. For ε≥ε_b, approaching Q_nc 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 ηδ=1, where the temperature at the bifurcation point also diverges. The background potential V_eff^bg(r) develops an infinite barrier at r=0 without local extrema, acting as a perfect repeller. In contrast, the photon potential V_eff^ph(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_nc, for ε<ε_b, both geometries support horizonless structures above Q_ext; for ε≥ε_b, only the optical geometry does so in the region Q_nc<Q<Q_m^ph. 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.
ER -