Abstract

This study delves into the dynamics of phantom anti-de Sitter black holes within a massive gravity framework, providing a comprehensive examination of the interplay between thermodynamic principles and gravitational dynamics. We investigate Joule-Thomson expansions and their implications for black hole thermodynamics, revealing how variations in temperature and pressure affect gas behavior relative to the horizon radius. Our analysis of the Joule-Thomson coefficients shows that smaller black holes exhibit positive coefficients indicative of gas expansion during cooling, while larger black holes display negative coefficients associated with heating behaviors. We further explore the corrected entropy of black holes, noting oscillations in smaller charged black holes that stabilize with larger horizon radii, while phantom energy configurations exhibit significant differences in stability characteristics. Our assessment of Helmholtz free energy, internal energy, enthalpy, and Gibbs free energy highlights contrasting stability trends between charged and phantom-AdS black holes, with the former displaying stable thermodynamic properties and the latter indicating increased instability at low charges and horizon radii. Additionally, the analysis of effective potential dynamics reveals critical insights into the stability of the innermost stable circular orbits for test particles. We demonstrate that the innermost stable circular orbit behavior in both charged and phantom-AdS black holes is significantly influenced by parameters χ<inf>1</inf> and χ<inf>2</inf>, illustrating the complex relationship between black hole properties and orbital dynamics. In summary, our findings elucidate the intricate relationship between thermodynamics and gravitational behavior in black hole systems, particularly regarding the unique effects of phantom energy.