Research on the universal scaling law of black hole supercritical thermodynamics has made progress

In the past two decades, research on black hole thermodynamics has revealed the similarity between black holes and fluid systems—the existence of a small black hole-large black hole first-order phase transition in charged Anti-de Sitter (AdS) black holes. However, a key question remains unresolved - what thermodynamic behavior does a black hole exhibit in the "supercritical" region above the critical point? For a long time, people have known little about this, and the existing supercritical phase transition lines are not universal.

Recently, the Institute of Theoretical Physics, Chinese Academy of Sciences published the supercritical thermodynamic phase transition lineL±Application to black hole thermodynamics. The research team completed numerical verification on six black hole models and seven different critical points, covering complex systems such as four-dimensional and high-dimensional Reissner-Nordström-AdS black holes, hairy black holes, Gauss-Bonnet black holes and Barrow fractal black holes. The results show thatL±Lines obey universal scaling laws in these systems.

Research points out that, unlike a single supercritical phase transition line such as the Widom line or the Frenkel line,L±The line divides the supercritical region into three intervals: the small black hole phase, the indistinguishable phase and the large black hole phase, showing universal scaling behavior. More importantly, this universal scale still holds true in complex systems beyond the description of van der Waals fluids, such as hairy black holes with two critical points, or Barrow black holes modified by quantum gravitational effects.

该研究在非扩展相空间中将黑洞热力学与液—液相变建立类比。在非扩展相空间中，温度被视为外部场，熵则作为序参量。研究发现，这类黑洞的相图具有负斜率共存线，正是液—液相变的特征标志。类比于液—液相变是熵驱动而非能量驱动，这为理解黑洞热力学行为提供了新视角。

This framework is applicable to conventional black hole systems and provides new tools for exploring quantum gravitational effects.

Relevant research results were published inResearch上。研究工作得到国家自然科学基金、国家重点研发计划、中国博士后科学基金等的支持。

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