Oscillatory dynamics around black hole in f(R,T) gravity coupled with Euler–Heisenberg nonlinear electrodynamics

In this work, we analyze a class of static and spherically symmetric black hole (BH) configurations within the framework of [Formula: see text] gravity coupled to Euler–Heisenberg nonlinear electrodynamics. By systematically deriving the modified field equations, we determine the associated metric function and examine how higher-order electromagnetic corrections, together with matter-geometry coupling terms, influence the resulting spacetime geometry. The physical characteristics of the obtained BH solution are investigated through the behavior of the metric function and its explicit dependence on the model parameters. Furthermore, we investigate the dynamics of neutral test particles in this background by constructing the effective potential, identifying the criteria for stable circular orbits, and computing the innermost stable circular orbits (ISCOs). The analysis is further developed by studying particle trajectories, which provides a detailed description of the geodesic structure of the spacetime. In this case, we consider small perturbations around circular geodesics and evaluate the corresponding harmonic oscillation frequencies in both the local reference frame and for distant observers. In this context, the results illustrate nontrivial deviations from standard BH models arising from the combined contributions of modified gravity and nonlinear electrodynamics, leading to a more complete description of strong-field gravitational effects.

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