Black hole thermodynamics and particle motion in f(R,T)–NLED gravity

This research examines the thermodynamic characteristics and trajectories of particles surrounding a charged black hole within the framework of [Formula: see text] gravity combined with nonlinear electrodynamics. It evaluates how the parameters [Formula: see text], [Formula: see text], and [Formula: see text] introduce gravitational and electromagnetic adjustments beyond the scope of general relativity. The paper concentrates on the lapse function [Formula: see text], demonstrating that the count of black hole horizons may increase to three or four, contingent on whether [Formula: see text] is positive or negative. We assess thermodynamic aspects including the mass function, Hawking temperature, and thermal stability. A positive [Formula: see text] creates an environment akin to de Sitter space, which reduces temperature and phase transitions, while a negative [Formula: see text] (similar to AdS) enhances confinement and promotes Hawking–Page-type transitions. The coupling parameter [Formula: see text] intensifies the effective cosmological term, leading to a decrease in [Formula: see text] and overall stability. Additionally, we investigate the effective potential, angular momentum, energy, and stability of the circular orbit of a time-like particle. This study reveals alternating stability zones for circular orbits and demonstrates how alterations in gravity and nonlinear electrodynamics modify the spacetime curvature encountered by particles in orbit.