Thermodynamic Features of Ads Black Holes within Rastall Gravity and Perfect Fluid Matter Framework

In this study, we delve into the analysis of phase transitions by employing approximated formulas for the horizon radius. The novelty of this work is apparent in the first-time determination of analytical expressions for critical points for charged and Kerr-Newman Anti-de Sitter (AdS) black holes within Rastall gravity, considering the presence of perfect fluid matter. This paves the way for exploring the distinctiveness of fractional order phase transitions in these AdS black holes. Additionally, the analysis involves calculating critical exponents, offering insights into the behavior of crucial thermodynamic quantities near the inflection point. The examination of how perfect fluid matter influences phase transitions reveals various critical behaviors, demonstrating that the variation in phase transition is contingent on the intensity of perfect fluid matter. Notably, this variation is portrayed by a linearly increasing trajectory with the escalation of this intensity.