Particle motion and thermal fluctuations of charged AdS black holes surrounded by exotic fluid with modified Chaplygin equation of state

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This study explores the intricate relationships between thermodynamic properties and particle dynamics of charged AdS black holes, emphasizing the impacts of charge Q and higher-order corrections, particularly the parameter β, which is a modified Chaplygin gas parameter. Our analysis of entropy reveals that smaller black holes exhibit decreasing entropy variations with increased β, while larger black holes display a complex behavior characterized by initial entropy increases followed by decreases as the horizon radius expands. The Helmholtz free energy analysis suggests that higher-order corrections significantly modify energy behavior, indicating potential phase transitions influenced by gravitational forces, with increasing β values counteracting instability linked to larger charges. Internal energy assessments show an evolving stability of black holes, transitioning from negative to positive values as entropy increases, while also highlighting the destabilizing effects of electric charge. The specific heat analysis illustrates a complex thermal stability regime, where a rise in specific heat with increasing Q correlates with greater stability. However, critical points of instability arise with higher B values, where B is the BH model parameter. Moreover, the trajectories of particles around non-rotating charged black holes reveal that lower parameters result in unbounded motion. In contrast, higher parameters tend to restrict particles closer to the event horizon. Collectively, these findings underscore the complex interplay among charge, higher-order corrections, and stability in black hole thermodynamics, shedding light on the fundamental mechanisms governing black hole behavior and paving the way for future explorations using advanced models and simulations.