Thermodynamics of five-dimensional Schwarzschild black holes in the canonical ensemble

André, Rui; Lemos, José P. S.

doi:10.1103/physrevd.102.024006

“…This Gibbs free energy should be considered as the generalized canonical free energy, where the horizon radius r + can take all values from zero to infinity because r + is taken as the order parameter to describe the microscopic degrees of freedom [50]. This type of the generalized free energy has been applied to investigate and understand the physical process of the phase transitions in the Schwarzschild black holes [62,63]. In this way, we can then formulate the free energy landscape for the RNAdS black holes.…”

Section: Jhep10(2020)090mentioning

confidence: 99%

Thermal dynamic phase transition of Reissner-Nordström Anti-de Sitter black holes on free energy landscape

Li

¹

,

Zhang

²

,

Wang

³

2020

J. High Energ. Phys.

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We explore the thermodynamics and the underlying kinetics of the van der Waals type phase transition of Reissner-Nordström anti-de Sitter (RNAdS) black holes based on the free energy landscape. We show that the thermodynamic stabilities of the three branches of the RNAdS black holes are determined by the underlying free energy landscape topography. We suggest that the large (small) RNAdS black hole can have the probability to switch to the small (large) black hole due to the thermal fluctuation. Such a state switching process under the thermal fluctuation is taken as a stochastic process and the associated kinetics can be described by the probabilistic Fokker-Planck equation. We obtained the time dependent solutions for the probabilistic evolution by numerically solving Fokker-Planck equation with the reflecting boundary conditions. We also investigated the first passage process which describes how fast a system undergoes a stochastic process for the first time. The distributions of the first passage time switching from small (large) to large (small) black hole and the corresponding mean first passage time as well as its fluctuations at different temperatures are studied in detail. We conclude that the mean first passage time and its fluctuations are related to the free energy landscape topography through barrier heights and temperatures.

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“…This Gibbs free energy should be considered as the generalized canonical free energy, where the horizon radius r + can take all values from zero to infinity because r + is taken as the order parameter to describe the microscopic degrees of freedom [43]. This type of the generalized free energy has been applied to investigate and understand the physical process of the phase transitions in the Schwarzschild black holes [56,57]. In this way, we can then formulate the free energy landscape for the RNAdS black holes.…”

Section: Free Energy Landscapementioning

confidence: 99%

Thermal Dynamic Phase Transition of Reissner-Nordström Anti-de Sitter Black Holes on Free Energy Landscape

Li,

Zhang,

Wang

2020

Preprint

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We explore the thermodynamics and the underlying kinetics of the van der Waals type phase transition of Reissner-Nordström anti-de Sitter (RNAdS) black holes based on the free energy landscape. We show that the thermodynamic stabilities of the three branches of the RNAdS black holes are determined by the underlying free energy landscape topography. We suggest that the large (small) RNAdS black hole can have the probability to switch to the small (large) black hole due to the thermal fluctuation. Such a state switching process under the thermal fluctuation is taken as a stochastic process and the associated kinetics can be described by the probabilistic Fokker-Planck equation. We obtained the time dependent solutions for the probabilistic evolution by numerically solving Fokker-Planck equation with the reflecting boundary conditions. We also investigated the first passage process which describes how fast a system undergoes a stochastic process for the first time. The distributions of the first passage time switching from small (large) to large (small) black hole and the corresponding mean first passage time as well as its fluctuations at different temperatures are studied in detail. We conclude that the mean first passage time and its fluctuations are related to the free energy landscape topography through barrier heights and temperatures.

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“…By making restrictions, in particular with respect to the horizon topology, one can generalize Einstein-Maxwell theory to five dimensions [44][45][46][47][48][49]. In the context of mimetic gravity, one can get the final form of 5-dimensional version of Einstein-Maxwell field equations as well as scalar field equation by setting D = 5 in Eqs.…”

Section: Solutions In Five Dimensionsmentioning

confidence: 99%

Higher dimensional charged static and rotating solutions in mimetic gravity

Bakhtiarizadeh

2021

Preprint

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We find new solutions to the Einstein-Maxwell equations in the presence of mimetic field in D dimensions, all of which are asymptotically anti-de Sitter (AdS) space-times. We first derive the solutions in 5-dimensional spacetime, in detail. Then, by extending our calculations to six and seven dimensions, we will obtain a general form for solutions in D > 4 dimensions. The results describe electrically charged static and rotating solutions, which have spherical, toroidal or cylindrical horizons and depending on their global identifications can be regarded as black holes, or black strings/branes. Some physical properties of solutions such as horizons, singularities as well as entropy, mass and angular momenta of rotating solutions are also investigated.

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Thermodynamics of five-dimensional Schwarzschild black holes in the canonical ensemble

Cited by 32 publications

References 17 publications

Thermal dynamic phase transition of Reissner-Nordström Anti-de Sitter black holes on free energy landscape

Thermal dynamic phase transition of Reissner-Nordström Anti-de Sitter black holes on free energy landscape

Thermal Dynamic Phase Transition of Reissner-Nordström Anti-de Sitter Black Holes on Free Energy Landscape

Higher dimensional charged static and rotating solutions in mimetic gravity

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