Cosmological model from the holographic equipartition law with a modified Rényi entropy

Komatsu, Nobuyoshi

doi:10.1140/epjc/s10052-017-4800-2

Cited by 146 publications

(143 citation statements)

References 131 publications

(235 reference statements)

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“…The results indicate that, compared with the Newtonian regime, the gravitational potential energy of the cloud is decreased when EUP is valid, leading to growth in the Jeans mass. It has been argued that since gravity is a long-range interaction, one may use the Rényi entropy formalism to study the gravitational systems (Komatsu 2017 14) is valid in both the EUP and Rényi frameworks. Hence, the EUP results, obtained in this paper, are also available in the framework of Rényi entropy (one just needs to replace 4β in the results of second section with δπ to obtain the corresponding results in the Rényi formalism).…”

Section: Discussionmentioning

confidence: 99%

The generalized and extended uncertainty principles and their implications on the Jeans mass

Moradpour

Ziaie

Ghaffari

et al. 2019

Monthly Notices of the Royal Astronomical Society: Letters

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The generalized and extended uncertainty principles affect the Newtonian gravity and also the geometry of the thermodynamic phase space. Under the influence of the latter, the energy-temperature relation of ideal gas may change. Moreover, it seems that the Newtonian gravity is modified in the framework of the Rényi entropy formalism motivated by both the long-range nature of gravity, and the extended uncertainty principle. Here, the consequences of employing the generalized and extended uncertainty principles, instead of the Heisenberg uncertainty principle, on the Jeans mass are studied. The results of working in the Rényi entropy formalism are also addressed. It is shown that unlike the extended uncertainty principle and the Rényi entropy formalism which lead to the same increase in the Jeans mass, the generalized uncertainty principle can decrease it. The latter means that a cloud with mass smaller than the standard Jeans mass, obtained in the framework of the Newtonian gravity, may also undergo the gravitational collapse process.

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Section: Discussionmentioning

confidence: 99%

The generalized and extended uncertainty principles and their implications on the Jeans mass

Moradpour

Ziaie

Ghaffari

et al. 2019

Monthly Notices of the Royal Astronomical Society: Letters

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“…Interestingly, in the explicit form of the expression determining γ , it is the Rényi entropy formula for black holes [as defined in (22)] which arises. In another recent work [56], our Tsallis-Rényi model has been considered in a cosmological setup describing the difference between the degrees of freedom on the surface and in the bulk in a closed region of space. It has been found that the corresponding Padmanabhan's "holographic equipartition law" [57] can result an effective cosmological constant in the model.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics

Czinner

Iguchi

2017

Eur. Phys. J. C

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Thermodynamics of rotating black holes described by the Rényi formula as equilibrium and zeroth law compatible entropy function is investigated. We show that similarly to the standard Boltzmann approach, isolated Kerr black holes are stable with respect to axisymmetric perturbations in the Rényi model. On the other hand, when the black holes are surrounded by a bath of thermal radiation, slowly rotating black holes can also be in stable equilibrium with the heat bath at a fixed temperature, in contrast to the Boltzmann description. For the question of possible phase transitions in the system, we show that a HawkingPage transition and a first order small black hole/large black hole transition occur, analogous to the picture of rotating black holes in AdS space. These results confirm the similarity between the Rényi-asymptotically flat and Boltzmann-AdS approaches to black hole thermodynamics in the rotating case as well. We derive the relations between the thermodynamic parameters based on this correspondence.

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“…In this context, we assume an arbitrary entropy on the horizon, extending the previous works [29,30] (in which particular entropies were used). In the present study, we apply the arbitrary entropy to the holographic equipartition model, in order to universally examine thermodynamic constraints on an extra driving term in cosmological equations for a flat Friedmann-Robertson-Walker (FRW) universe at late times.…”

Section: Introductionmentioning

confidence: 99%

Generalized thermodynamic constraints on holographic-principle-based cosmological scenarios

Komatsu

2019

Phys. Rev. D

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The holographic principle can lead to cosmological scenarios, i.e., holographic equipartition models. In this model, an extra driving term (corresponding to a time-varying cosmological term) in cosmological equations depends on an associated entropy on the horizon of the universe. The driving term is expected to be constrained by the second law of thermodynamics, as if the cosmological constant problem could be discussed from a thermodynamics viewpoint. In the present study, an arbitrary entropy on the horizon, SH , is assumed, extending previous analysis based on particular entropies [Phys. Rev. D 96, 103507 (2017)]. The arbitrary entropy is applied to the holographic equipartition model, in order to universally examine thermodynamic constraints on the driving term in a flat Friedmann-Robertson-Walker universe at late times. The second law of thermodynamics for the holographic equipartition model is found to constrain the upper limit of the driving term, even if the arbitrary entropy is assumed. The upper limit implies that the order of the driving term is likely consistent with the order of the cosmological constant measured by observations. An approximately equivalent upper limit can be obtained from the positivity of SH in the holographic equipartition model. 98.80.Es, 95.30.Tg

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Cosmological model from the holographic equipartition law with a modified Rényi entropy

Cited by 146 publications

References 131 publications

The generalized and extended uncertainty principles and their implications on the Jeans mass

The generalized and extended uncertainty principles and their implications on the Jeans mass

Thermodynamics, stability and Hawking–Page transition of Kerr black holes from Rényi statistics

Generalized thermodynamic constraints on holographic-principle-based cosmological scenarios

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