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

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.