Thermodynamic curvature in phase transitions for Hayward AdS black hole

TL;DR

The study analyzes the Hayward-AdS black hole in extended black hole thermodynamics, focusing on $P$-$V$ criticality and microscopic structure via Ruppeiner geometry. The authors derive the equation of state and identify a van der Waals–like critical point, obtaining the mean-field critical exponents $\left(\alpha,\beta,\gamma,\delta\right)=(0,\tfrac{1}{2},1,3)$ and confirming standard scaling laws. Using a normalized thermodynamic curvature $R_{\rm N}$, they show $R_{\rm N}$ diverges to $-\infty$ at criticality and remains negative along the coexistence curve, indicating dominant attractive interactions, with a sign change and possible repulsion away from criticality; two temperatures $\widetilde{T}_{div}$ and $\widetilde{T}_{0}$ characterize the microstructure, both of which are dimension-independent near the critical point. Collectively, these results reinforce the utility of extended phase space thermodynamics and thermodynamic geometry in unveiling the microphysical properties of regular AdS black holes and their universal critical behavior.

Abstract

We investigate $P$-$V$ criticality, with a focus on Ruppeiner geometry, in the extended phase space of Hayward anti-de Sitter (AdS) black holes. Through thermodynamic analysis, we confirm that Hayward-AdS black holes undergo distinct $P$-$V$ phase transitions and exhibit well-defined critical phenomena in the vicinity of their critical points. These behaviors are characterized by four critical exponents that typically obey the scaling laws predicted by mean-field theory--indicating a consistent thermodynamic framework with classical phase transition systems ($e.g.,$ van der Waals fluids). Furthermore, we employ Ruppeiner geometry to probe the thermodynamic fluctuations of Hayward-AdS black holes, and by calculating the corresponding curvature scalar, we gain direct insights into the interaction nature of the black hole's microscopic constituents.

Figures (3)

• Figure 1: $\widetilde{P}$-$\widetilde{V}$ phase diagram of Hayward-AdS black hole for different temperatures with $\alpha=0.2, G_{\rm N}=1$.
• Figure 2: Normalized Curvature Scalar $R_{\rm N}$ of Hayward-AdS Black Holes: Behavior along the coexistence phase of small and large black holes for dimensions $D=5,6,7,8$. Here we set $\alpha=0.2, G_{\rm N}=1.$
• Figure 3: Hayward-AdS black hole:(a) The divergence curves of $R_{\rm N}$; (b) The sign changing curves of $R_{\rm N}$. Here we set $\alpha=0.2, G_{\rm N}=1.$