Confining nonlinear electrodynamics black holes: from thermodynamic phases to high-frequency phenomena with accretion process

TL;DR

This work analyzes a static, confining nonlinear electrodynamics black hole whose metric is asymptotically Schwarzschild with a characteristic $Q^3/(9\xi^2 r^4)$ near-field correction and no $Q^2/r^2$ Reissner–Nordström term. The authors derive horizon structure, embedding diagrams, lensing (including vacuum, plasma, and axion-plasmon media), gravitational redshift, and extended thermodynamics (Joule-Thomson expansion and heat capacity), revealing parameter-dependent phase behavior. They compute the photon sphere and shadow via geodesic analysis and Lyapunov exponents, and perform fully relativistic BHL accretion simulations that show a ~40% boost in accretion rate and HFQPOs with stable $3:2$ and $2:1$ ratios without spin. Overall, the results supply multiple observational channels—lensing, shadow size, QPO spectra, and accretion dynamics—to test the confining NED BH against current and future astrophysical data, providing a spin-independent mechanism for high-frequency QPOs.

Abstract

We investigate a static, spherically symmetric black hole solution arising from Einstein gravity coupled to a confining nonlinear electrodynamics model that reproduces Maxwell theory in the strong-field regime while introducing confinement-like corrections at large distances. The resulting metric function is asymptotically Schwarzschild but carries a characteristic Q^3/(9ξ^2 r^4) correction, where $Q$ is the magnetic charge and $ξ$ is the nonlinear electrodynamics parameter, with the conventional Reissner-Nordström term Q^2/r^2 absent. We analyze the horizon structure and construct three-dimensional embedding diagrams to visualize spatial geometry. Using the Gauss-Bonnet theorem, we compute the weak-field deflection angle in vacuum, cold plasma, and axion-plasmon media, finding that the nonlinear electromagnetic corrections reduce the total bending compared to Schwarzschild at fixed Arnowitt-Deser-Misner mass. The gravitational redshift, Joule-Thomson expansion coefficient, and heat capacity are derived, revealing phase transitions and inversion curves that depend on the model parameters. We obtain closed-form expressions for the photon sphere radius, Lyapunov exponent, and shadow size, demonstrating their sensitivity to Q and $ξ$ along observable Intensities. Fully relativistic hydrodynamical simulations of Bondi-Hoyle-Lyttleton accretion show that the confining geometry produces a $\sim 40\%$ enhancement in mass accretion rate relative to Schwarzschild and generates quasi-periodic oscillations with stable 3:2 and 2:1 frequency ratios matching observations from black hole X-ray binaries. These results establish the confining nonlinear electrodynamics black hole as a testable model that can reproduce high-frequency quasi-periodic oscillation pairs without invoking black hole spin.

Figures (14)

• Figure 1: Metric function $f(r)$ for the confining NED BH with fixed Schwarzschild mass $M=1$. Representative parameter combinations are displayed with different line styles and colors. The black dotted horizontal line marks $f(r)=0$. Horizon locations correspond to zero crossings, with NE configurations exhibiting two distinct horizons, Ext cases showing degenerate horizons, and NS cases displaying no horizon. The absence of the standard RN $Q^2/r^2$ term results in asymptotically Schwarzschild behavior at large $r$.
• Figure 2: Three-dimensional embedding diagrams of the confining NED BH with metric function $f(r) = 1 - 2M_{\text{ADM}}/r + Q^3/(9\xi^2 r^4)$, where $M = 1$ is fixed and $M_{\text{ADM}} = M + \frac{2\sqrt{2}}{3} \xi Q^{3/2} \ln(2\xi\sqrt{2Q})$. Each panel displays a turquoise surface representing the isometric embedding from the EH $r_H$ to $r = 12$, a black spiral depicting an infalling test particle trajectory, and a red ring marking the EH location. Panels (i)--(iii) illustrate the effect of increasing $Q$ at fixed $\xi=1.0$: larger magnetic charge yields progressively wider throat geometries and larger horizon radii. Comparing panels (ii) and (iv) reveals the influence of $\xi$ at fixed $Q=1.0$: reducing $\xi$ decreases the contribution of the ADM mass and consequently shrinks the radius of the horizon.
• Figure 3: Deflection angle $\Theta$ as a function of the impact parameter $b$ and the NED parameter $\xi$, for fixed values $M=1$ and $Q=0.5$. Larger $\xi$ increases the ADM mass and slightly enhances the bending, while increasing $b$ reduces $\Theta$ following the characteristic inverse power-law behavior.
• Figure 4: Plasma-corrected deflection angle $\tilde{\Theta}$ as a function of the impact parameter $b$ and the plasma parameter $\delta$, for fixed values $M=1$, $\xi=1$, and $Q=0.5$. Increasing $\delta$ (corresponding to denser plasma or lower photon frequency) enhances the total bending, while the characteristic $1/b$ decay persists at large impact parameters.
• Figure 5: Gravitational redshift $z_\infty$ as a function of the emission radius $r_e$ and the NED parameter $\xi$, for fixed values $M=1$ and $Q=0.5$. The redshift increases steeply near the EH and decreases at large $r_e$, recovering the weak-field limit. The variation with $\xi$ reflects the competition between the enhanced ADM mass and the suppressed NED correction term.