Thermodynamic geometry and phase transitions in Kerr-Newman-AdS black holes

Sahay, Anurag; Sarkar, Tapobrata; Sengupta, Gautam

doi:10.1007/jhep04(2010)118

Cited by 77 publications

(71 citation statements)

References 44 publications

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“…A novel result was also revealed in Ref. [20]: the isothermal line in an R-P diagram shows a self-crossing behaviour, leading some authors to suggest that such a crossing point can be approximately treated as the phase transition point. In this section we give a brief view of the thermodynamics of the VdW fluid, examine the relationship between the Ruppeiner geometry and the liquid-gas phase transition, and reveal the critical phenomena associated with the scalar curvature.…”

Section: Van Der Waals Fluidmentioning

confidence: 72%

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

Wei¹,

Liu²,

Mann³

2019

Phys. Rev. D

121

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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Section: Van Der Waals Fluidmentioning

confidence: 72%

“…Another interesting behaviour of the scalar curvature was observed for a VdW fluid [20]. 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.…”

mentioning

confidence: 80%

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

Wei¹,

Liu²,

Mann³

2019

Phys. Rev. D

121

113

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show abstract

“…It turned out that the canonical ensemble admits a first order small-large black hole phase transition which is in many respects analogous to the liquid-gas phase transition in fluids. This triggered wide interest and various comparisons to the Van der Waals critical behaviour were studied, e.g., [22,[28][29][30] and references therein. In this appendix we recapitulate this interesting analogy and relate it to the results in the extended phase space performed in this paper.…”

Section: Appendix: Van Der Waals Analogymentioning

confidence: 99%

P − V criticality of charged AdS black holes

Kubizňák

Mann

2012

J. High Energ. Phys.

1,128

1,183

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Treating the cosmological constant as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume, we reconsider the critical behaviour of charged AdS black holes. We complete the analogy of this system with the liquid-gas system and study its critical point, which occurs at the point of divergence of specific heat at constant pressure. We calculate the critical exponents and show that they coincide with those of the Van der Waals system.

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“…Ruppeiner's (and Weinhold's) geometric approach to thermodynamics has been kindled recently in black hole thermodynamics [15,17,[20][21][22]26,[28][29][30][31][32]. The main goal of this standpoint is to analyze the scalar curvature of Ruppeiner's metrics for different "macroscopic" thermodynamic models of black holes, in order to obtain a hint via Ruppeiner's conjecture of the interactions that a microscopic model of gravity might involve.…”

Section: Riemannian-geometrical Approach To Black Hole Thermodynamicsmentioning

confidence: 99%

Geometric Thermodynamics: Black Holes and the Meaning of the Scalar Curvature

García-Ariza

Montesinos

Castillo

2014

Entropy

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In this paper we show that the vanishing of the scalar curvature of Ruppeiner-like metrics does not characterize the ideal gas. Furthermore, we claim through an example that flatness is not a sufficient condition to establish the absence of interactions in the underlying microscopic model of a thermodynamic system, which poses a limitation on the usefulness of Ruppeiner's metric and conjecture. Finally, we address the problem of the choice of coordinates in black hole thermodynamics. We propose an alternative energy representation for Kerr-Newman black holes that mimics fully Weinhold's approach. The corresponding Ruppeiner's metrics become degenerate only at absolute zero and have non-vanishing scalar curvatures.

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Thermodynamic geometry and phase transitions in Kerr-Newman-AdS black holes

Cited by 77 publications

References 44 publications

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

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

P − V criticality of charged AdS black holes

Geometric Thermodynamics: Black Holes and the Meaning of the Scalar Curvature

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