Testing the Weak Gravity Conjecture via Gravitational Lensing, Black Hole Shadows, and Barrow Thermodynamics in F(R)-Euler-Heisenberg (A)dS Black Holes

TL;DR

This paper explores the relationship between the Weak Gravity Conjecture and cosmic censorship in complex black hole models, using gravitational lensing, shadows, and thermodynamics to reveal universal and novel insights into black hole physics.

Contribution

It introduces a universal entropy--extremality relation and demonstrates the compatibility of WGC and WCCC in $F(R)$-Euler-Heisenberg black holes through multiple analytical approaches.

Findings

Photon sphere radius is independent of the cosmological background.

Black hole shadow images are constructed under isotropic accretion.

Van der Waals-like phase transitions are observed in Barrow entropy framework.

Abstract

We investigate the interplay of the Weak Gravity Conjecture (WGC) and the Weak Cosmic Censorship Conjecture (WCCC) in $F(R)$-Euler-Heisenberg black holes in Anti-de Sitter and de Sitter backgrounds. The solution is characterized by the electric charge $q$, the $F(R)$ deviation $f_{R_0}$, the Euler--Heisenberg coupling $\lambda$, and the constant scalar curvature $R_0$. We establish a universal entropy--extremality relation that provides thermodynamic evidence for the WGC independently of $f_{R_0}$ and $R_0$. Photon sphere analysis from both geodesic and topological perspectives confirms the simultaneous compatibility of the WGC and WCCC, with the Euler--Heisenberg coupling restoring photon spheres in the naked singularity regime. Gravitational lensing in the strong- and weak-deflection limits reveals that the photon sphere radius is independent of the cosmological background while the critical impact parameter nearly doubles in de Sitter. Black hole shadow images under isotropic accretion are constructed. Within the Barrow entropy framework, we uncover van der Waals-type phase transitions and analyze Joule-Thomson expansion, identifying the small black hole phase as the WGC-compatible thermodynamic regime accessible via isenthalpic cooling.