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

TL;DR

We study Einstein–Born–Infeld–AdS black holes by integrating thermodynamic analysis, quantum corrections, gravitational lensing, and holographic heat-engine perspectives. The work derives the classical Hawking temperature and incorporates GUP-induced and exponential entropy corrections, analyzes gravitational redshift and lensing in vacuum and plasma via the Gauss–Bonnet theorem, and examines heat-engine performance in extended phase space, showing BI corrections are generically tiny ($\sim 10^{-12}$) except in the strong-field near-horizon regime where $r_h \lesssim 1.5$ (Planck units). BI effects scale as $a^{4}/r^{n}$ with $n \ge 5$, confining observable signatures to the near-horizon region and requiring extreme precision for detection; nonetheless, explicit expressions for the deflection, redshift, and cycle efficiencies are provided, offering concrete targets for future high-precision tests in strong gravity. The unified framework clarifies where nonlinear electrodynamics and quantum corrections leave detectable imprints and points to extensions (rotation, alternative nonlinear theories, Gauss–Bonnet couplings) that could enhance observational prospects.

Abstract

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.

Figures (14)

• Figure 1: [$\Lambda=0$, $Q=0$, $a=0$] Schwarzschild BH ($r_H=2$)
• Figure 2: [$\Lambda=0$, $Q=0.5$, $a=0$] Charged EBI BH ($r_H=1.8666197$)
• Figure 3: [$\Lambda=-0.1$, $Q=0.5$, $a=0.5$] Charged EBI-AdS BH ($r_H=1.6917351$)
• Figure 4: [$\Lambda=0.1$, $Q=0.5$, $a=1.0$] Charged EBI-dS BH ($r_H=3.8749683$)
• Figure 6: [$\Lambda=0$, $a=0$] Reissner-Nordström BH.