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Modified Gravity: From Black Holes Entropy to Current Cosmology III

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Astrophysics, Cosmology, and Black Holes".

Deadline for manuscript submissions: closed (28 February 2022) | Viewed by 9532

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Dr. Kazuharu Bamba

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Guest Editor

Faculty of Symbiotic Systems Science, Fukushima University, Fukushima 960-1296, Japan
Interests: particle cosmology; gravity theory; inflation; late time acceleration
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Recent cosmological observations strongly support that the current expansion of the universe is accelerating. The origin of such a cosmic acceleration mechanism is one of the most significant problems in modern cosmology. Indeed, this is shown by the fact that the Nobel Prize in Physics 2011 was presented to the finding of the current cosmic acceleration by means of the observations of the Type Ia supernovae.

There are two representative approaches to explain the current accelerated expansion of the universe. One is to introduce “dark energy” in the framework of general relativity. The other is to modify a gravitational theory, such as F(R) gravity, so that we can obtain so-called geometrical dark energy. It is believed that a modified gravitational theory must pass cosmological bounds and solar system tests because it corresponds to an alternative theory of gravitation to general relativity. As another meaningful touchstone of modified gravity, it is important to examine whether the second law of thermodynamics can be satisfied in the models of modified gravity.

The fundamental connection between gravitation and thermodynamics has been suggested by the discovery of black hole thermodynamics with black hole entropy and Hawking temperature. In addition, it was shown that the Einstein equation can be derived from the proportionality of the entropy to the horizon area together with the Clausius relation in thermodynamics. This consequence has been applied to various cosmological settings as well as modified gravitational theories. In particular, the connections between thermodynamics and modified gravity have recently been discussed extensively.

In this special issue, we discuss the application of thermodynamics to the test of a successful alternative gravitational theory to general relativity. Through this procedure, we can obtain a clue to resolve the dark energy problem “geometrically”. It is considered that any successful modified gravity theory should obey the second law of thermodynamics. If the second law is violated in certain universes in a model, it is more likely to be due to an incorrect generalization of the second law or some inherent inconsistency of the model itself. For the latter case, the model should be abandoned. It is strongly expected that the considerations of this special issue can produce our new physical understanding on entropy in the context of the relation between thermodynamics and gravitation and shed light on novel ingredients as well as insights on modern cosmology, in particular new properties of dark energy.

Prof. Dr. Kazuharu Bamba
Guest Editor

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Keywords

Quantum aspects of black holes, evaporation, thermodynamics
Black hole entropy
Modified theories of gravity
Dark energy
Cosmology

Published Papers (5 papers)

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Research

9 pages, 566 KiB

Open AccessArticle

Constraints on Non-Flat Starobinsky f(R) Dark Energy Model

by Chao-Qiang Geng, Yan-Ting Hsu and Jhih-Rong Lu

Entropy 2021, 23(10), 1320; https://doi.org/10.3390/e23101320 - 10 Oct 2021

Viewed by 1409

Abstract

We study the viable Starobinsky

f (R)

dark energy model in spatially non-flat FLRW backgrounds, where [...] Read more.

We study the viable Starobinsky

f (R)

dark energy model in spatially non-flat FLRW backgrounds, where

f (R) = R - λ R_{c h} [1 - {(1 + R^{2} / R_{c h}^{2})}^{- 1}]

with

R_{c h}

and

λ

representing the characteristic curvature scale and model parameter, respectively. We modify CAMB and CosmoMC packages with the recent observational data to constrain Starobinsky

f (R)

gravity and the density parameter of curvature

Ω_{K}

. In particular, we find the model and density parameters to be

λ^{- 1} < 0.283

at 68% C.L. and

Ω_{K} = - 0 . 00099_{- 0.0042}^{+ 0.0044}

at 95% C.L., respectively. The best

χ^{2}

fitting result shows that

χ_{f (R)}^{2} ≲ χ_{Λ C D M}^{2}

, indicating that the viable

f (R)

gravity model is consistent with

Λ

CDM when

Ω_{K}

is set as a free parameter. We also evaluate the values of AIC, BIC and DIC for the best fitting results of

f (R)

and

Λ

CDM models in the non-flat universe. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology III)

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Figure 1

22 pages, 930 KiB

Open AccessEditor’s ChoiceArticle

Impact of Thermal Fluctuations on Logarithmic Corrected Massive Gravity Charged Black Hole

by Abdul Jawad, Shahid Chaudhary and Kazuharu Bamba

Entropy 2021, 23(10), 1269; https://doi.org/10.3390/e23101269 - 28 Sep 2021

Cited by 5 | Viewed by 1379

Abstract

We investigate the influence of the first-order correction of entropy caused by thermal quantum fluctuations on the thermodynamics of a logarithmic corrected charged black hole in massive gravity. For this black hole, we explore the thermodynamic quantities, such as entropy, Helmholtz free energy, internal energy, enthalpy, Gibbs free energy and specific heat. We discuss the influence of the topology of the event horizon, dimensions and nonlinearity parameter on the local and global stability of the black hole. As a result, it is found that the holographic dual parameter vanishes. This means that the thermal corrections have no significant role to disturb the holographic duality of the logarithmic charged black hole in massive gravity, although the thermal corrections have a substantial impact on the thermodynamic quantities in the high-energy limit and the stability conditions of black holes. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology III)

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Figure 1

17 pages, 495 KiB

Open AccessArticle

Higher Dimensional Rotating Black Hole Solutions in Quadratic f(R) Gravitational Theory and the Conserved Quantities

by Gamal G. L. Nashed and Kazuharu Bamba

Entropy 2021, 23(3), 358; https://doi.org/10.3390/e23030358 - 17 Mar 2021

Cited by 4 | Viewed by 2027

Abstract

We explore the quadratic form of the

f (R) = R + b R^{2}

gravitational theory to derive rotating N-dimensions black hole solutions with

a_{i}, i \geq 1

rotation parameters. Here, R is the Ricci scalar and [...] Read more.

We explore the quadratic form of the

f (R) = R + b R^{2}

gravitational theory to derive rotating N-dimensions black hole solutions with

a_{i}, i \geq 1

rotation parameters. Here, R is the Ricci scalar and b is the dimensional parameter. We assumed that the N-dimensional spacetime is static and it has flat horizons with a zero curvature boundary. We investigated the physics of black holes by calculating the relations of physical quantities such as the horizon radius and mass. We also demonstrate that, in the four-dimensional case, the higher-order curvature does not contribute to the black hole, i.e., black hole does not depend on the dimensional parameter b, whereas, in the case of

N > 4

, it depends on parameter b, owing to the contribution of the correction

R^{2}

term. We analyze the conserved quantities, energy, and angular-momentum, of black hole solutions by applying the relocalization method. Additionally, we calculate the thermodynamic quantities, such as temperature and entropy, and examine the stability of black hole solutions locally and show that they have thermodynamic stability. Moreover, the calculations of entropy put a constraint on the parameter b to be

b < \frac{1}{16 Λ}

to obtain a positive entropy. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology III)

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Figure 1

25 pages, 530 KiB

Open AccessArticle

Early Universe Thermodynamics and Evolution in Nonviscous and Viscous Strong and Electroweak Epochs: Possible Analytical Solutions

by Abdel Nasser Tawfik and Carsten Greiner

Entropy 2021, 23(3), 295; https://doi.org/10.3390/e23030295 - 28 Feb 2021

Cited by 7 | Viewed by 2075

Abstract

Based on recent perturbative and non-perturbative lattice calculations with almost quark flavors and the thermal contributions from photons, neutrinos, leptons, electroweak particles, and scalar Higgs bosons, various thermodynamic quantities, at vanishing net-baryon densities, such as pressure, energy density, bulk viscosity, relaxation time, and temperature have been calculated up to the TeV-scale, i.e., covering hadron, QGP, and electroweak (EW) phases in the early Universe. This remarkable progress motivated the present study to determine the possible influence of the bulk viscosity in the early Universe and to understand how this would vary from epoch to epoch. We have taken into consideration first- (Eckart) and second-order (Israel–Stewart) theories for the relativistic cosmic fluid and integrated viscous equations of state in Friedmann equations. Nonlinear nonhomogeneous differential equations are obtained as analytical solutions. For Israel–Stewart, the differential equations are very sophisticated to be solved. They are outlined here as road-maps for future studies. For Eckart theory, the only possible solution is the functionality,

H (a (t))

, where

H (t)

is the Hubble parameter and

a (t)

is the scale factor, but none of them so far could to be directly expressed in terms of either proper or cosmic time t. For Eckart-type viscous background, especially at finite cosmological constant, non-singular

H (t)

and

a (t)

are obtained, where

H (t)

diverges for QCD/EW and asymptotic EoS. For non-viscous background, the dependence of

H (a (t))

is monotonic. The same conclusion can be drawn for an ideal EoS. We also conclude that the rate of decreasing

H (a (t))

with increasing

a (t)

varies from epoch to epoch, at vanishing and finite cosmological constant. These results obviously help in improving our understanding of the nucleosynthesis and the cosmological large-scale structure. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology III)

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Figure 1

11 pages, 810 KiB

Open AccessArticle

Horizon Thermodynamics in D-Dimensional f(R) Black Hole

by Chenrui Zhu and Rong-Jia Yang

Entropy 2020, 22(11), 1246; https://doi.org/10.3390/e22111246 - 02 Nov 2020

Cited by 2 | Viewed by 1568

Abstract

We consider whether the new horizon-first law works in higher-dimensional

f (R)

theory. We firstly obtain the general formulas to calculate the entropy and the energy of a general spherically-symmetric black hole in D-dimensional

f (R)

theory. For [...] Read more.

We consider whether the new horizon-first law works in higher-dimensional

f (R)

theory. We firstly obtain the general formulas to calculate the entropy and the energy of a general spherically-symmetric black hole in D-dimensional

f (R)

theory. For applications, we compute the entropies and the energies of some black hokes in some interesting higher-dimensional

f (R)

theories. Full article

(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology III)

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