Insight into the Microstructures of Black Holes with Quantum-Triggered Violations

TL;DR

This work applies Ruppeiner thermodynamic geometry to charged AdS black holes with quantum conformal anomaly, exploring how the central charge $\alpha_{ m c}$ and electric charge $Q$ modify $P$-$V$ criticality and the microscopic structure. By computing coexisting volumes and the normalized thermodynamic curvature $R_N$ across three parameter regimes ($\alpha_c\le 0$, $0<\alpha_c< Q^{2}/8$, and $\alpha_c=Q^{2}/8$), the authors reveal universal critical behavior with a $t^{2}$ scaling of $R_N$ at criticality and regime-dependent coefficients, including $-\tfrac{1}{8}$ for $\alpha_c\le 0$ and $-2\pm\sqrt{3}$ or other values for the quantum-anomalous cases. They demonstrate that quantum conformal anomaly can induce multiple critical points, temperature-independent singularities, and sign changes in microstructure interactions, providing geometric fingerprints of quantum-corrected black hole thermodynamics. The results offer a geometric window into the microscopic degrees of freedom of quantum-corrected spacetimes and suggest universal features that may extend to other quantum-gravity-inspired black hole systems.

Abstract

In this study, we investigate the microstructures of a charged AdS (Anti-de Sitter) black hole exhibiting quantum anomalies through the lens of Ruppeiner geometry. Previous research has established that black holes undergo $P$-$V$ phase transitions and exhibit critical phenomena near their critical points, characterized by four critical exponents that typically obey scaling laws predicted by mean-field theory. However, recent findings have revealed that black holes with quantum anomalies can violate these scaling laws. Motivated by these discoveries, we employ Ruppeiner geometry to probe the thermodynamic fluctuations and gain insights into the microstructure of such black holes. Our analysis aims to elucidate how quantum effects modify the microscopic properties of spacetime, offering a novel perspective on the understanding of black hole thermodynamics.

Figures (11)

• Figure 1: Isotherms in the $\widetilde{P}$-$\widetilde{V}$ plane for the reduced equation of state of a charged AdS black hole with quantum conformal anomaly, with $\widetilde{T}=T/T_{\rm c}$. The green, red, and dashed blue curves correspond to $\widetilde{T}=1.1$, $\widetilde{T}=1$, and $\widetilde{T}=0.9$, respectively, with $\alpha_{\rm c}=-0.5$ and $Q=1$ fixed throughout all plots.
• Figure 2: Coexistence curves of small and large black hole phases in the $\widetilde{T}$-$\widetilde{V}$ diagram for charged AdS black holes with quantum anomaly. Here we set $\alpha_{\rm c}=-0.5, Q=1$.
• Figure 3: The normalized thermodynamic curvature $R_{\rm N}$ of the charged AdS black hole with quantum anomaly for $\alpha_{\rm c} < 0$ along the coexistence small and large phases. Here we set $\alpha_{\rm c}=-0.5, Q=1$.
• Figure 4: $\widetilde{P}$-$\widetilde{V}$ isotherms for the reduced equation of state of a quantum-anomalous charged AdS black hole. Curves correspond to normalized temperatures $\widetilde{T}=T/T_{\rm c}$: dashed red ($\widetilde{T}=0.8$), dashed blue ($\widetilde{T}=0.9$), dashed black ($\widetilde{T}=1$), solid black ($\widetilde{T}=1$), solid green ($\widetilde{T}=1.1$), solid red ($\widetilde{T}=1.2$). Dashed curves are plotted via Eq.(\ref{['crit']}), while solid curves are via Eq.(\ref{['crit20']}). Parameters are set as $\alpha_{\rm c}=0.1$ and $Q=1$.
• Figure 5: The coefficients $a_{ij}$ as a function of $\alpha_{\rm c}$ in the range $(0, {Q^{2}}/{8}]$. Here, we set $Q=1$.