P-V criticality in the extended phase space of Gauss-Bonnet black holes in AdS space (1306.6233v4)

Abstract: We study the $P-V$ criticality and phase transition in the extended phase space of charged Gauss-Bonnet black holes in anti-de Sitter space, where the cosmological constant appears as a dynamical pressure of the system and its conjugate quantity is the thermodynamic volume of the black hole. The black holes can have a Ricci flat ($k=0$), spherical ($k=1$), or hyperbolic ($k=-1$) horizon. We find that for the Ricci flat and hyperbolic Gauss-Bonnet black holes, no $P-V$ criticality and phase transition appear, while for the black holes with a spherical horizon, even when the charge of the black hole is absent, the $P-V$ criticality and the small black hole/large black hole phase transition will appear, but it happens only in $d=5$ dimensions; when the charge does not vanish, the $P-V$ criticality and the small black hole/large phase transition always appear in $d=5$ dimensions; in the case of $d\ge 6$, to have the $P-V$ criticality and the small black hole/large black hole phase transition, there exists an upper bound for the parameter $b=\widetilde{\alpha}|Q|^{-2/(d-3)}$, where $\tilde {\alpha}$ is the Gauss-Bonnet coefficient and $Q$ is the charge of the black hole. We calculate the critical exponents at the critical point and find that for all cases, they are the same as those in the van der Waals liquid-gas system.

• The paper demonstrates that spherical Gauss-Bonnet black holes in five dimensions exhibit P-V phase transitions, even in the absence of charge.
• The analysis reveals that in dimensions six and higher, the emergence of P-V criticality depends on an upper bound of the parameter b linked to the Gauss-Bonnet term.
• Critical exponents matching those of the van der Waals liquid-gas system underline a universal thermodynamic behavior bridging gravitational and statistical physics.

P-V Criticality in the Extended Phase Space of Gauss-Bonnet Black Holes in AdS Space

The paper "P-V criticality in the extended phase space of Gauss-Bonnet black holes in AdS space" by Rong-Gen Cai, Li-Ming Cao, Li Li, and Run-Qiu Yang investigates thermodynamic properties of charged Gauss-Bonnet black holes in Anti-de Sitter (AdS) space, focusing on the P-V criticality and phase transitions within an extended phase space framework. This research leverages the conceptualization of the cosmological constant as a dynamic pressure and its conjugate quantity as the thermodynamic volume of black holes.

Overview of Key Findings

• P-V Criticality and Phase Transitions: The analysis particularly emphasizes that for Gauss-Bonnet black holes with Ricci flat and hyperbolic horizons, there is no occurrence of P-V criticality or phase transitions. For spherical horizons, the paper finds that even without charge, P-V criticality and small/large black hole transitions can occur in five dimensions (d=5). With non-zero charge, these phase transitions consistently appear in five dimensions.
• Dimensional Dependency: In dimensions equal or greater than six (d ≥ 6), the occurrence of P-V criticality and transitions is contingent on an upper bound of the parameter $b=\widetilde{\alpha}|Q|^{-2/(d-3)}$. Here, $\widetilde{\alpha}$ represents the Gauss-Bonnet coefficient and $Q$ the charge. This upper bound's existence is attributed to the influence of the Gauss-Bonnet term.
• Critical Exponents: The research determines that the critical exponents at the critical point for Gauss-Bonnet black holes match those found in the van der Waals liquid-gas system, emphasizing a remarkable analogy and universal characteristics shared between these systems.

Implications

This investigation into high-dimensional Gauss-Bonnet black holes broadens the understanding of black hole thermodynamics, especially in the context of extended phase space frameworks. By demonstrating P-V criticality in these black holes, the paper provides insights into the implications of incorporating higher curvature corrections, such as the Gauss-Bonnet term, on black hole thermodynamics.

The implications of this research stretch beyond theoretical interest. Understanding phase transitions in black holes could influence future models in cosmology and fundamental physics, particularly in string theory and its variants, where higher curvature terms are considered. The revelation of universal critical properties shared with classical thermodynamic systems could enhance the dialogue between gravitational and statistical thermodynamics.

Future Directions

The findings encourage further exploration of phase transitions in other variants of modified gravity theories, potentially extending the established analogies to other classes of solutions and broader settings. Additionally, further theoretical exploration is warranted to translate these findings into observational predictions, paving the way for potential empirical implications. Understanding how these phase transitions manifest in an observable universe could refine theoretical predictions about black hole chemistry, and perhaps offer insights into the unification of quantum mechanics and gravity.

In summary, the paper makes significant strides in understanding the thermodynamic behavior of higher-dimensional black holes in Gauss-Bonnet gravity. It provides a firm base for continued research into thermodynamic stability and phase transitions in various gravitational theories, strengthening the bridge between classical thermodynamics and black hole physics.