Analytical Critical Phenomena of Rotating Regular AdS Black Holes with Dark Energy

This study focuses on precisely calculating analytical critical points for rotating regular AdS black holes, examining scenarios with and without external dark field contributions. Importantly, it represents the first attempt to compute critical points for this specific class of rotating black holes. Our primary focus is on investigating the impact resulting from variations in the charge of nonlinear electrodynamics on the critical phenomena of rotating regular AdS black holes, while also incorporating the influence of quintessence field contributions. The analytical investigation is concentrated on the horizon radius, employing two distinct approaches to simplify the complexity and length of the calculations. Furthermore, our examination extends to deciphering the intricate relationship between dark energy and critical phenomena. This involves visually portraying a range of critical behaviors and detailing a recent discovery regarding how the intensity of quintessence affects phase transitions. The shift in these transitions conform to either a concave or convex function, a characteristic dependent on the sign of quintessence intensity.