Correspondence of phase transition points and singularities of thermodynamic geometry of black holes

Mansoori, Seyed Ali Hosseini; Mirza, Behrouz

doi:10.1140/epjc/s10052-013-2681-6

Cited by 88 publications

(63 citation statements)

References 24 publications

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“…This result shows that the scalar curvature of Quevedo metric can not be used to uniquely predict the second order phase transition of extended charged Hořava-Lifshitz black hole. A similar result has been obtained for phantom Reissner-Nordeström-AdS black hole [54].…”

Section: Singularities In Thermodynamic Geometrysupporting

confidence: 87%

Phase transition and thermodynamic stability in extended phase space and charged Hořava–Lifshitz black holes

Poshteh

Riazi

2017

Gen Relativ Gravit

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For charged black holes in Hořava-Lifshitz gravity, a second order phase transition takes place in extended phase space where the cosmological constant is taken as thermodynamic pressure. We relate the second order nature of phase transition to the fact that the phase transition occurs at a sharp temperature and not over a temperature interval. Once we know the continuity of the first derivatives of the Gibbs free energy, we show that all the Ehrenfest equations are readily satisfied. We study the effect of the perturbation of the cosmological constant as well as the perturbation of the electric charge on thermodynamic stability of Hořava-Lifshitz black hole. We also use thermodynamic geometry to study phase transition in extended phase space. We investigate the behavior of scalar curvature of Weinhold, Ruppeiner, and Quevedo metric in extended phase space of charged Hořava-Lifshitz black holes. It is checked if these curvatures could reproduce the result of specific heat for the phase transition.

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Section: Singularities In Thermodynamic Geometrysupporting

confidence: 87%

Phase transition and thermodynamic stability in extended phase space and charged Hořava–Lifshitz black holes

Poshteh

Riazi

2017

Gen Relativ Gravit

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“…In particular, refs. [63,64] has investigated the relation between the divergence of the scalar curvature of thermodynamical geometry in different ensembles and the singularity of heat capacities.…”

Section: Jhep02(2015)143mentioning

confidence: 99%

Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS5 × S5 spacetime

Zhang

Cai

2015

J. High Energ. Phys.

114

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Abstract:We study the thermodynamics and thermodynamic geometry of a five-dimensional Schwarzschild AdS black hole in AdS 5 × S 5 spacetime by treating the cosmological constant as the number of colors in the boundary gauge theory and its conjugate quantity as the associated chemical potential. It is found that the chemical potential is always negative in the stable branch of black hole thermodynamics and it has a chance to be positive, but appears in the unstable branch. We calculate the scalar curvatures of the thermodynamical Weinhold metric, Ruppeiner metric and Quevedo metric, respectively and we find that the scalar curvature in the Weinhold metric is always vanishing, while in the Ruppeiner metric the divergence of the scalar curvature is related to the divergence of the heat capacity with fixed chemical potential, and in the Quevedo metric the divergence of the scalar curvature is related to the divergence of the heat capacity with fixed number of colors and to the vanishing of the heat capacity with fixed chemical potential.

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“…The purpose of this viewpoint is twofold: on the one hand, it intends to relate the divergences of heat capacities (often regarded as thermodynamic critical points) to geometric singularities of Weinhold's metric structure; on the other, it is aimed to determine the nature of the interactions involved in microscopic models of gravity via Ruppeiner's conjecture. Regarding the former issue, the aforementioned relationship has been established under the usual scheme of black hole thermodynamics, where the mass of black holes is regarded as the analogue of energy, whereas the corresponding deformation coordinates are taken to be angular momentum and charge [17,18]. Nonetheless, we share the point of view that this choice is somewhat arbitrary and may be challenged on both mathematical and physical grounds [19,20].…”

Section: Introductionmentioning

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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Correspondence of phase transition points and singularities of thermodynamic geometry of black holes

Cited by 88 publications

References 24 publications

Phase transition and thermodynamic stability in extended phase space and charged Hořava–Lifshitz black holes

Phase transition and thermodynamic stability in extended phase space and charged Hořava–Lifshitz black holes

Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS5 × S5 spacetime

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

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