Thermal aspects and particle dynamics of Euler-Heisenberg AdS black hole in 4D Einstein Gauss-Bonnet gravity

TL;DR

The paper investigates charged AdS black holes in the regularized 4D Einstein-Gauss-Bonnet framework coupled to Euler-Heisenberg nonlinear electrodynamics, addressing how higher-curvature and QED corrections modify black-hole physics. Using the regularized 4D EGB approach and the weak-field EH limit, it constructs an exact static solution with metric function $F(r)$ dependent on $M$, $Q$, $\\Lambda$, $a$, and $\alpha$. Thermodynamics in the extended phase space reveals a logarithmic entropy correction $S = \pi r_+^2 + 4 \alpha \ln r_+$ and a critical behavior largely governed by $\alpha$, with milder EH corrections; Joule-Thomson expansion shows nontrivial cooling/heating regions influenced by $Q$, $a$, and $\alpha$. The geodesic analysis demonstrates significant modifications to effective potentials, orbital frequencies, and ISCO due to GB and EH terms, highlighting a rich interplay between higher-curvature gravity and nonlinear electrodynamics with potential extensions to quasinormal modes, shadows, and rotating solutions.

Abstract

We construct charged AdS black hole solutions in four dimensional Einstein Gauss Bonnet gravity coupled to Euler Heisenberg nonlinear electrodynamics and investigate their physical properties. The modified field equations admit black hole solutions whose horizon structure is significantly affected by higher-curvature and nonlinear electromagnetic corrections, allowing for multiple horizons depending on the model parameters. In the extended phase space, where the cosmological constant is interpreted as thermodynamic pressure, we analyze the thermodynamic behavior and show that both the Gauss Bonnet coupling and the Euler Heisenberg parameter induce notable modifications in the equation of state, critical behavior, and thermal stability. Interpreting the black hole mass as enthalpy, we study the Joule-Thomson expansion and determine the inversion temperature and pressure, demonstrating that higher curvature and nonlinear electrodynamic effects substantially influence the cooling and heating regions. Finally, we examine time-like geodesics and show that Gauss Bonnet corrections significantly modify the effective potential, orbital stability, and particle motion in the strong-field regime

Figures (21)

• Figure 1: $a=0.5$
• Figure 2: $\alpha=0.3$
• Figure 4: $a=0.6$
• Figure 5: $\alpha=0.3$
• Figure 7: $a=0.6$