Microscopic explanation for black hole phase transitions via Ruppeiner geometry: Two competing factors–the temperature and repulsive interaction among BH molecules

Chen, Yong; Li, Haitang; Zhang, Shaojun

doi:10.1016/j.nuclphysb.2019.114752

Cited by 28 publications

(17 citation statements)

References 89 publications

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“…So the application of the Ruppeiner geometry into black hole thermodynamics makes it possible to glimpse the underlying microstructure of black holes from macroscopic thermodynamic quantities. With the help of Ruppeiner geometry, interesting features are observed in other black hole systems [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57]. Especially, in some situations that the entropy and thermodynamic volume of these black holes are not independent, such as Schwarzchild-AdS black hole, Reissner-Nordström AdS (RN-AdS) black hole and etc., the heat capacity at constant volume of the black hole becomes zero.…”

Section: Introductionmentioning

confidence: 99%

Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity

Wang

et al. 2021

Eur. Phys. J. C

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The phase transition and thermodynamic geometry of a 4-dimensional AdS topological charged black hole in de Rham, Gabadadze and Tolley (dRGT) massive gravity have been studied. After introducing a normalized thermodynamic scalar curvature, it is speculated that its value is related to the interaction between the underlying black hole molecules if the black hole molecules exist. We show that there does exist a crucial parameter given in terms of the topology, charge, and massive parameters of the black hole, which characterizes the thermodynamic properties of the black hole. It is found that when the parameter is positive, the singlet large black hole phase does not exist for sufficient low temperature and there is a weak repulsive interaction dominating for the small black hole which is similar to the Reissner–Nordström AdS black hole; when the parameter is negative, an additional phase region describing large black holes also implies a dominant repulsive interaction. These constitute the distinguishable features of dRGT massive topological black hole from those of the Reissner–Nordström AdS black hole as well as the Van der Waals fluid system.

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Section: Introductionmentioning

confidence: 99%

Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity

Wang

et al. 2021

Eur. Phys. J. C

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“…This yielded the first insight into black hole microstructure. This approach has since been generalized to other black hole systems [50][51][52][53][54][55][56][57][58].…”

mentioning

confidence: 99%

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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“…By studying the behaviour of the Gibbs free energy versus the temperature for fixed pressure, the phase structure and transitions of the system can be depicted which have been studied thoroughly in Refs. [56][57][58]61]. The full P − T phase diagram is rather diverse depending on the set of free parameters (q, α, β, b).…”

Section: Phase Transitions In Born-infeld-dilaton Black Holementioning

confidence: 99%

“…Following Ref. [61], we fix q = 0.2, b = 1 and β = 2 to study the effect of α on the phase diagram. It should be noted that α < 1 to ensure the positivity of the Hawking temperature.…”

Section: Phase Transitions In Born-infeld-dilaton Black Holementioning

confidence: 99%

Photon orbits and phase transitions in Born-Infeld-dilaton black holes

Chen

Zhang

2020

Nuclear Physics B

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Relations between photon orbits and thermodynamical phase transitions are explored in Born-Infeld-dilaton-AdS black hole. The coupling between the electromagnetic field and the dialton field is chosen such that the full phase diagram contains zeroth-order and first-order phase transitions as well as RPT. We find that there exist non-monotonic beahviors of the photon orbit radius rps and the minimum impact parameter ups which signal the existence of the various phase transitions. In particular, the marginal value of pressure under which RPT occur can be read off from these behaviors. Along the co-existing lines, there are changes of both rps and ups, whose dependence on the transition temperature show characteristic behaviors signalling the existence of RPT. Moreover, the critical exponents of ∆rps and ∆ups are found to take a universal value 1 2 . These results imply that rps and ups can be used as order parameters to describe BH phase transitions.

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Microscopic explanation for black hole phase transitions via Ruppeiner geometry: Two competing factors–the temperature and repulsive interaction among BH molecules

Cited by 28 publications

References 89 publications

Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity

Ruppeiner geometry and thermodynamic phase transition of the black hole in massive gravity

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

Photon orbits and phase transitions in Born-Infeld-dilaton black holes

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