Critical phenomena and thermodynamic geometry of charged Gauss-Bonnet AdS black holes

Abstract: In this paper, we study the phase structure and equilibrium state space geometry of charged topological Gauss-Bonnet black holes in $d$-dimensional anti-de Sitter spacetime. Several critical points are obtained in the canonical ensemble, and the critical phenomena and critical exponents near them are examined. We find that the phase structures and critical phenomena drastically depend on the cosmological constant $\Lambda$ and dimensionality $d$. The result also shows that there exists an analogy between the black hole and the van der Waals liquid gas system. Moreover, we explore the phase transition and possible property of the microstructure using the state space geometry. It is found that the Ruppeiner curvature diverges exactly at the points where the heat capacity at constant charge of the black hole diverges. This black hole is also found to be a multiple system, i.e., it is similar to the ideal gas of fermions in some range of the parameters, while to the ideal gas of bosons in another range.

• The paper demonstrates that including the Gauss-Bonnet term in AdS black holes reveals van der Waals-like phase transitions with critical exponents α=0, β=1/2, γ=1, and δ=3.
• The analysis employs canonical ensemble methods and Ruppeiner geometry to examine how dimensionality and the cosmological constant affect the black holes' phase structure.
• The findings provide a foundation for future research linking classical thermodynamics and quantum gravity through advancements in AdS/CFT correspondence.

Analyzing the Critical Phenomena and Thermodynamic Geometry of Charged Gauss-Bonnet AdS Black Holes

The study conducted on the thermodynamic properties of $d$-dimensional charged topological Gauss-Bonnet anti-de Sitter (AdS) black holes enhances our understanding of the intricate connection between black hole thermodynamics and classical thermodynamic systems. This analysis delineates the phase structure and the equilibrium state space geometry of these black holes, focusing on the behavior in the canonical ensemble. By incorporating the Gauss-Bonnet term, the research explores the impact of higher-dimensional space and the cosmological constant ($\Lambda$) on critical phenomena.

Phase Structure and Critical Phenomena

The investigation yields several critical points and examines the associated phenomena, emphasizing the pronounced influence of dimensionality ($d$) and the cosmological constant $\Lambda$. For $d = 6$, findings reveal multiple and varied behaviors contingent upon the value of $\Lambda$. Particularly interesting are the ranges $\Lambda \in (-\infty, -0.5) \cup (-0.4725, 0)$ and $\Lambda \in (-0.5, -0.4725)$, which manifest distinct phase structures. Notably, higher dimensions ($d \geq 7$) exhibit similar behaviors regardless of $\Lambda$, simplifying the analysis.

Analogies with Van der Waals Systems

A compelling insight from the study is the analogy between these black holes and van der Waals liquid-gas systems, particularly observable in the $Q$-$\Phi$ criticality that aligns closely with $P$-$V$ criticality in classical thermodynamics. The investigation identifies critical exponents similar to those of the van der Waals system, where the identified values are $\alpha = 0$, $\beta = 1/2$, $\gamma = 1$, and $\delta = 3$. Such findings affirm that the charged Gauss-Bonnet AdS black holes exhibit van der Waals-like phase transitions.

Implications for Theoretical Physics

This study not only parallels the behavior of classical systems but also enriches our theoretical understanding of black hole thermodynamics. The determination of parameters and critical exponents provides a foundation for further exploration in both classical thermodynamics and quantum gravity theories, contributing to a deeper comprehension of the AdS/CFT correspondence.

Geometrical Insights

The application of thermodynamic geometry, specifically the Ruppeiner geometry, is instrumental in understanding the microstructure of these black holes. The Ruppeiner curvature's divergence is consistent with the divergent behavior of the heat capacity at constant charge, highlighting potential phase transitions. Moreover, the sign of this curvature offers insights into the nature of interactions at a microscopic level, indicating a system with alternating attractive and repulsive interactions akin to ideal gases of bosons and fermions, respectively.

Future Prospects

Future research could expand upon these findings by exploring other forms of higher curvature corrections or extending analysis to non-canonical ensembles. Additionally, bridging these theoretical results with empirical data might provide valuable tests for quantum gravity predictions. As exploration into the thermodynamic phase space of black holes continues, these findings lay crucial groundwork for the theoretical physics community.

The investigation into the charged Gauss-Bonnet AdS black holes thus advances our grasp of complex thermodynamic systems, reinforcing the analogy with classical systems while illuminating potential pathways for future theoretical advancements.