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.
Indrajit Halder (Tue,) studied this question.