Consistency between dynamical and thermodynamical stabilities for perfect fluid in f(R) theories

Fang, Xiongjun; He, Xiaokai; Jing, Jiliang

doi:10.1140/epjc/s10052-018-6053-0

Cited by 8 publications

(7 citation statements)

References 31 publications

(61 reference statements)

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“…Roupas proved that the maximum of total entropy of perfect fluid is consistent with the dynamical stability obtained by Yabushita [17,18]. More recently, we show that the dynamical stability and thermodynamical stability are exactly the same both in general relativity or some modified theory such as f (R) theories [19,20].…”

Section: Introductionsupporting

confidence: 86%

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Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

Yang,

Fang,

Jing

2021

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The entropy principle shows that, for self-gravitating perfect fluid, the Einstein field equations can be derived from the extrema of the total entropy, and the thermodynamical stability criterion are equivalent to the dynamical stability criterion. In this paper, we recast the dynamical criterion for the charged self-gravitating perfect fluid in Einstein-Maxwell theory, and further give the criterion of the star with barotropic condition. In order to obtain the thermodynamical stability criterion, first we get the general formula of the second variation of the total entropy for charged perfect fluid case, and then obtain the thermodynamical criterion for radial perturbation. We show that these two stability criterion are the same, which suggest that the inherent connection between gravity and thermodynamic even when the electric field is taken into account.

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Section: Introductionsupporting

confidence: 86%

“…are always satisfied, where T and χ are the temperature of the fluid and the redshift factor of the static observer. It is showed that if the Lagrangian constructed purely by the metric and its derivatives, the second variation of total entropy under the perturbation can be written as a uniform expression [19,20],…”

Section: Thermodynamic Methodsmentioning

confidence: 99%

Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

Yang,

Fang,

Jing

2021

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“…Thermodynamic descriptions of gravitational solutions at the event horizon and cosmological ones at the apparent horizon in F(R) gravity have been studied in series of papers [54][55][56][57][58][59][60][61][62] . In this work, we are going to evaluate thermodynamic phase transition of black hole solutions in a special class of F(R) gravity with constant Ricci scalar in which both F(R) and its derivative F R (R) are vanished in the field equations.…”

Section: Introductionmentioning

confidence: 99%

Thermal stability of a special class of black hole solutions in F(R) gravity

2019

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In this paper, we work on the topological Lifshitzlike black hole solutions of a special class of vacuum F(R)−gravity that are static and spherically symmetric. We investigate geometric and thermodynamic properties of the solutions with due respect to the validity of the first law of thermodynamics. We examine the van der Waals like behavior for asymptotically AdS solutions with spherical horizon by studying the P − v, G − T and C Q,P − r + diagrams and find a consistent result. We also investigate the same behavior for hyperbolic horizon and interestingly find that the system under study can experience a phase transition with negative temperature.

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“…Gao extended their work to an arbitrary perfect fluid in a static spherical geometry [16], in which they only used some thermodynamical relations. After that, this principle has been widely studied by the researchers [17][18][19][20][21][22]. Their results showed the consistency between the ordinary thermodynamics of fluid and gravitational dynamics.…”

Section: Introductionmentioning

confidence: 92%

Universality of entropy principle for a general diffeomorphism-covariant purely gravitational theory

Jiang,

Fang,

Gao

2021

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Thermodynamics plays an important role in gravitational theories. It is a principle independent of the gravitational dynamics, and there is still no rigorous proof to show that it is consistent with the dynamical principle. We consider a self-gravitating perfect fluid system in a general diffeomorphism-covariant purely gravitational theory. Based on the Noether charge method proposed by Iyer and Wald, considering static off/on-shell variational configurations which satisfy the gravitational constraint equation, we rigorously prove that the extrema of the total entropy of perfect fluid inside a compact region for fixed total particle number demands that the static configuration is an on-shell solution after we introduce some appropriate boundary conditions, i.e., it also satisfies the spatial gravitational equations. This means that the entropy principle of the fluid stores the same information as the gravitational equation in a static configuration. Our proof is universal and holds for any diffeomorphism-covariant purely gravitational theories, such as Einstein gravity, f (R) gravity, Lovelock gravity, f (Gauss-Bonnet) gravity and Einstein-Weyl gravity. Our result shows the consistency between the ordinary thermodynamics and the gravitational dynamics.

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Consistency between dynamical and thermodynamical stabilities for perfect fluid in f(R) theories

Cited by 8 publications

References 31 publications

Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

Consistency between dynamical and thermodynamical stabilities for charged self-gravitating perfect fluid

Thermal stability of a special class of black hole solutions in F(R) gravity

Universality of entropy principle for a general diffeomorphism-covariant purely gravitational theory

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