Characterized behaviors of black hole thermodynamics in the supercritical region

Abstract

The comprehension of universal thermodynamic behaviors in the supercritical region is crucial for examining the characteristics of black hole systems under high temperature and pressure. This study is devoted to the analysis of characteristic lines and crossover behaviors within the supercritical region. By making use of the free energy, we introduce three key thermodynamic quantities: scaled variance, skewness, and kurtosis. Our results demonstrate that the Widom line, associated with the maximal scaled variance, can effectively differentiate between small and large black hole-like subphases, each displaying distinct thermodynamic behaviors within the supercritical region. Furthermore, by utilizing quasinormal modes, we identify the Frenkel line, offering a dynamic perspective to distinguish between small and large black hole-like subphases. These contribute to a deeper comprehension of black hole subphases in the supercritical region, thus illuminating new facets of black hole thermodynamics.

Figures (3)

• Figure 1: Phase diagram for the charged AdS black hole. The black solid curve is the coexistence curve of the small and large black holes. The black dashed line represents the widom line, and the blue dashed line represents the Frenkel line. These lines divide the supercritical region into the small and large black hole-like subphases from the perspective of thermodynamics and dynamics, respectively.
• Figure 2: The behavior of the thermodynamic functions $\Omega$, $S\sigma$, and $\kappa\sigma^2$. (a) Behavior of the scaled variance $\Omega$ for different values of pressure. (b), (c), and (d) are the density plots of the scaled variance $\Omega$, skewness $S\sigma$, and kurtosis $\kappa\sigma^2$, respectively. The black hole charge $Q=1$. The black dashed line in (b) represents the Widom line. The cyan dashed lines indicate the points where $S\sigma$ and $\kappa\sigma^2$ are vanish in (c) and (d).
• Figure 3: The QNMs as a function of temperature at fixed pressures. The blue and red lines correspond to the monotonic and oscillatory modes, respectively. Here, the solid lines represent thermodynamically stable states, while the dashed lines represent thermodynamically metastable or unstable states. The black lines represent the phase transition point of first-order phase transition.