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<p>We investigate the interplay of the Weak Gravity Conjecture (WGC) and the Weak Cosmic Censorship Conjecture (WCCC) in <i>F</i>(<i>R</i>)-Euler-Heisenberg black holes in Anti-de Sitter and de Sitter backgrounds. The solution is characterized by the electric charge <i>q</i>, the <i>F</i>(<i>R</i>) deviation <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>f</mi> <msub> <mi>R</mi> <mn>0</mn> </msub> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {f}_{R_0} \)</EquationSource> </InlineEquation>, the Euler-Heisenberg coupling <i>λ</i>, and the constant scalar curvature <i>R</i><sub>0</sub>. We establish a universal entropy-extremality relation that provides thermodynamic evidence for the WGC independently of <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msub> <mi>f</mi> <msub> <mi>R</mi> <mn>0</mn> </msub> </msub> </math></EquationSource> <EquationSource Format="TEX">\( {f}_{R_0} \)</EquationSource> </InlineEquation> and <i>R</i><sub>0</sub>. 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.</p>

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Testing the weak gravity conjecture via gravitational lensing, black hole shadows, and Barrow thermodynamics in F(R)-Euler-Heisenberg (A)dS black holes

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  • 发表日期：

    2026年7月9日

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  • Saeed Noori Gashti,
  • İzzet Sakallı,
  • Erdem Sucu,
  • Mohammad Reza Alipour,
  • Ankit Anand,
  • Mohammad Ali S. Afshar,
  • Behnam Pourhassan,
  • Jafar Sadeghi

摘要

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 \( {f}_{R_0} \) , the Euler-Heisenberg coupling λ, and the constant scalar curvature R0. We establish a universal entropy-extremality relation that provides thermodynamic evidence for the WGC independently of f R 0 \( {f}_{R_0} \) and R0. 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.