Universal Supercritical Thermodynamics for Black Holes

We investigate thermodynamic crossovers for black holes in the supercritical regime beyond the critical point, where small and large black holes become indistinguishable from the conventional viewpoint. We establish a refined supercritical phase diagram that comprehensively characterizes the phases of small, large, and indistinguishable black holes, delineated by 2 supercritical crossover lines. The universal scaling laws of these crossover lines are fully verified using the thermodynamics of Reissner-Nordström-anti-de Sitter black holes in both the standard framework and the extended thermodynamic phase space, where the cosmological constant is treated as pressure, as well as in 4 other black hole systems. Analogies with supercritical crossovers observed in liquid-gas and liquid-liquid phase transitions are discussed. This work can be extended to more complex black hole backgrounds and offers valuable insights into the fundamental nature of black hole thermodynamics.