Critical phenomena and chemical potential of a charged AdS black hole

Wei, Shao-Wen; Liang, Bin; Liu, Yu-Xiao

doi:10.1103/physrevd.96.124018

Cited by 44 publications

(28 citation statements)

References 55 publications

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“…This result is also the same as that of Ref. [65]. In addition, we have another exponent (1 −P ) = 0.1142 × |1 −Ṽ | 1.9058 , for coexistence small black hole, 0.2318 × |1 −Ṽ | 2.0954 , for coexistence large black hole.…”

Section: Critical Exponentssupporting

confidence: 89%

Reduced thermodynamics and an exact phase transition of five-dimensional Kerr-AdS black holes with equal spin parameters

Wei

Liu

2019

Phys. Rev. D

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Multi-spinning higher dimensional Kerr-AdS black holes admit the stable small-large black hole phase transition of van der Waals type. In this paper, we study the exact critical phenomena and phase structure in five-dimensional spacetime. First, we examine the thermodynamic laws in the reduced parameter space and find that they are quite different from the conventional thermodynamic laws. Then based on the reduced laws, the phase structure in different parameter spaces is investigated. The stable and metastable black hole phases are clearly displayed. We present a highly accurate fitting formula for the coexistence curve of small and large black hole phases. Using this fitting formula, we examine the critical exponents when the black hole system approaches the critical point along the coexistence curve. Moreover, employing the dimensional analysis and symmetry analysis, we also give a numerical study of the critical point for the unequal spinning black holes.These results are very useful on further understanding the microstructure of the multi-spinning black holes in higher dimensional spacetime.where d is the number of spacetime dimensions and l is the AdS radius. Adopting such an interpretation, the P -v criticality was first examined in detail in Ref. [22]. The result shows that the P -v criticality, phase transition, and critical exponents are extremely similar to that of the VdW fluid. Subsequently, this study was extended to other AdS black holes, see and references therein. Remarkably, besides the phase transition of VdW type, some rich critical phenomena and phase transitions, such as the reentrant phase transition, triple point, isolated critical point, and λ-line phase transition were observed [35][36][37][38][39][40][41][42][43][44][45][46]. These investigations not only give us new insight into the black hole thermodynamics, but also enhance our understanding on the cosmological constant.Among the different AdS black holes, the rotating ones are more attractive. In a d =4 dimensional spacetime, a rotating Kerr AdS black hole demonstrates a small-large black hole phase transition of VdW type [23]. And when the dimension of the spacetime increases, some novel phase transitions of great interesting occur. For d ≥ 6, besides the small-large black hole phase transition, the singly spinning Kerr AdS black hole also yields a reentrant phase transitions [35]. In this case, the black hole can have a phase transition from a large black hole phase to a small one, and then back to the large black hole phase with the increase of the temperature or pressure. One of the phase transitions is first-order while another is zero-order. Moreover, for a six-dimensional multi-spinning Kerr AdS black hole, a triple point emerges in the phase diagram, which is very similar to the solid/liquid/gas phase transition of water [36]. Nevertheless, the analytic or exact study of the phase transition for the rotating Kerr AdS black hole is very difficult. The reason is that, different from the charged AdS black hole case, the entrop...

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Section: Critical Exponentssupporting

confidence: 89%

Reduced thermodynamics and an exact phase transition of five-dimensional Kerr-AdS black holes with equal spin parameters

Wei

Liu

2019

Phys. Rev. D

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“…In literature, the critical phenomenon and the phase transition of several AdS black holes in various gravitational setups have already been explored. The first order phase transition for five dimensional charged AdS black holes was investigated in [8]. Similar critical behavior was also observed for the AdS black hole in massive gravity [9].…”

Section: Introductionsupporting

confidence: 57%

Instability and phase transitions of a rotating black hole in the presence of perfect fluid dark matter

et al. 2020

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In this paper, we study the thermodynamic features of a rotating black hole surrounded by perfect fluid dark matter. We analyze the critical behavior of the black hole by considering the known relationship between pressure and cosmological constant. We show that the black hole admits a first order phase transition and, both rotation and perfect fluid dark matter parameters have a significant impact on the critical quantities. We also introduce a new ad hoc pressure related to the perfect fluid dark matter and find a first order van der Waals like phase transition. In addition, using the sixth order WKB method, we investigate the massless scalar quasinormal modes (QNMs) for the static spherically symmetric black hole surrounded by dark matter. Using the finite difference scheme, the dynamical evolution of the QNMs is also discussed for different values of angular momentum and overtone parameters.

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“…Taking the temperature and fluid density as parameter space variables, the Ruppeiner scalar curvature, plotted as a function of pressure for fixed temperature was found to have two divergent points and a self-crossing behaviour. This behaviour was later observed in other black hole systems [21][22][23]. Although it was suggested that similar self-crossing behaviour can be used to determine the phase transition point [24] for normal hydrogen (or even a black hole), this idea is still speculative.…”

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confidence: 88%

Ruppeiner geometry, phase transitions, and the microstructure of charged AdS black holes

Wei¹,

Liu²,

Mann³

2019

Phys. Rev. D

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126

113

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We present a novel approach for probing the microstructure of a thermodynamic system that combines thermodynamic phase transitions with the Ruppeiner scalar curvature. Originally considered for van der Waals fluids and charged black holes [Phys. Rev. Lett. 123, 071103 (2019)], we extend and generalize our approach to higher-dimensional charged AdS black holes. Beginning with thermodynamic fluctuations, we construct the line element of the Ruppeiner geometry and obtain a universal formula for the scalar curvature R. We first review the thermodynamics of a van der Waals fluid and calculate the coexistence and spinodal curves. From this we are able to clearly display the phase diagram. Notwithstanding the invalidity of the equation of state in the coexistence phase regions, we find that the scalar curvature is always negative for the van der Waals fluid, indicating that attractive interactions dominate amongst the fluid microstructures. Along the coexistence curve, the scalar curvature R decreases with temperature, and goes to negative infinity at a critical temperature. We then numerically study the critical phenomena associated with the scalar curvature, and find that the critical exponent is 2, and that R(1 −T ) 2 C v ≈ 1/8, whereT and C v are the respective reduced temperature and heat capacity. We next consider four-dimensional charged AdS black holes. Vanishing of the heat capacity at constant volume yields a divergent scalar curvature. In order to extract the corresponding information, we define a new scalar curvature that has behaviour similar to that of a van der Waals fluid. We analytically confirm that at the critical point of the small/large black hole phase transition, the scalar curvature has a critical exponent 2, and R(1 −T ) 2 C v = 1/8, the same as that of a van der Waals fluid. However we also find a significant distinction: the scalar curvature can be positive for the small charged AdS black hole, implying that repulsive interactions dominate among the black hole microstructures. We then generalize our study to higher-dimensional charged AdS black holes, and investigate the influence of the dimensionality on the black hole microstructures and the scalar curvature. Our novel approach provides a universal way for probing the microstructure of charged AdS black holes from a geometric construction.

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Critical phenomena and chemical potential of a charged AdS black hole

Cited by 44 publications

References 55 publications

Reduced thermodynamics and an exact phase transition of five-dimensional Kerr-AdS black holes with equal spin parameters

Reduced thermodynamics and an exact phase transition of five-dimensional Kerr-AdS black holes with equal spin parameters

Instability and phase transitions of a rotating black hole in the presence of perfect fluid dark matter

Ruppeiner geometry, phase transitions, and the microstructure of charged AdS black holes

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