Born-Infeld signatures in AdS black hole thermodynamics and gravitational lensing

We investigate the thermodynamic and optical properties of Einstein-Born-Infeld-Anti-de Sitter (EBI-AdS) black holes (BHs). Our study derives the Hawking temperature using standard surface gravity methods and examines quantum corrections through both the Generalized Uncertainty Principle (GUP) and exponential entropy modifications, showing enhanced thermal radiation and potential remnant formation scenarios. The gravitational redshift analysis separates contributions from mass, cosmological constant, electromagnetic charge, and Born-Infeld (BI) corrections, with the latter scaling as $a^4/r^6$ and thus confined to near-horizon regimes. Using the Gauss-Bonnet theorem, we calculate light deflection angles in both vacuum and plasma environments, demonstrating how dispersive media can either enhance or suppress nonlinear electrodynamic signatures depending on observational configurations. The thermodynamic analysis in extended phase space, where the BH mass corresponds to enthalpy, reveals phase structures with heat capacity transitions between positive and negative values, indicating regions of local stability and instability sensitive to parameter choices. We study BH heat engines operating in rectangular thermodynamic cycles, achieving efficiencies of $η\sim 0.11$–$0.21$ that reach 30–61% of the corresponding Carnot limits, consistent with other AdS BH systems. Comparison with Johnson’s analysis confirms that BI corrections to heat engine efficiency are of order $10^{-12}$ for typical parameter ranges, though these effects become appreciable in the strong-field regime where $r_h \lesssim 1.5$ in Planck units. The plasma deflection analysis reveals frequency-dependent refractive modifications encoded in the plasma parameter, offering additional possible observational channels.

💡 Research Summary

This paper presents a comprehensive study of Einstein‑Born‑Infeld‑Anti‑de Sitter (EBI‑AdS) black holes, focusing on their thermodynamic behavior, quantum corrections, gravitational redshift, light‑deflection in both vacuum and plasma, and the performance of black‑hole heat engines.
First, the authors derive the metric function (f(r)) for a static, spherically symmetric EBI‑AdS spacetime. The Born‑Infeld (BI) parameter (a=\sqrt{\lambda|Q|}) enters through an integral function (h(r/a)) that yields a correction term proportional to (a^{4}/r^{6}). In the large‑radius limit the metric reduces to the familiar Reissner‑Nordström‑AdS form, while the (r^{-6}) term encodes the nonlinear electrodynamic effects that become relevant only near the horizon.
Using the standard surface‑gravity definition (\kappa=\frac12 f’(r_h)), the Hawking temperature is obtained as
\