On stability of the Kasner solution in quadratic gravity

Toporensky, A. V.; Müller, Daniel

doi:10.1007/s10714-016-2172-9

Cited by 14 publications

(13 citation statements)

References 42 publications

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“…After we submitted the first version of this work to arXiv we learned about a similar investigation [29]. The results of numerical analysis in this work concern the non-linear case and are qualitatively the same as ours, that are also close to those of the earlier paper [13], which did not link the study of the dynamics of anisotropies with the problem of massive ghosts in higher derivative gravity. The correspondence between the three independent investigations are certainly adding an extra safety to our conclusions.…”

Section: Asymptotic Series Expansion For Singular Perturbationsupporting

confidence: 76%

“…where the vector y includes σ, β ± and also first, second and third derivatives of these functions. Substituting into this system the expansion (13), we arrive at the equations for the power series…”

Section: Asymptotic Series Expansion For Singular Perturbationmentioning

confidence: 99%

“…Since the pioneering work [11], the Bianchi I metric have been extensively studied as a model of anisotropic homogeneous cosmology. For cosmologic solutions and stability in fourth derivative gravity, see recent works [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

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Beyond the linear analysis of stability in higher derivative gravity with the Bianchi-I metric

2019

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The study of stability of gravitational perturbations in higher derivative gravity has shown that at the linear level the massive unphysical ghost is not generated from vacuum if the initial seed of metric perturbation has frequency essentially below the Planck threshold. The mathematical knowledge indicated that the linear stability is supposed to hold even at the nonperturbative level, but in such a complicated case it is important to perform a verification of this statement. We compare the asymptotic stability solutions at the linear and full nonperturbative levels for the Bianchi-I metric with small anisotropies, which can be regarded as an extreme, zero frequency limit of a gravitational wave. As one should expect from the combination of previous analysis and general mathematical theorems, there is a good correspondence between linear stability and the nonperturbative asymptotic behavior.

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Section: Asymptotic Series Expansion For Singular Perturbationsupporting

confidence: 76%

Section: Asymptotic Series Expansion For Singular Perturbationmentioning

confidence: 99%

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Beyond the linear analysis of stability in higher derivative gravity with the Bianchi-I metric

2019

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“…However, since the phase space has two additional dimensions in comparison with GR, a Kasner solution in quadratic gravity may be in some situations unstable [7,8].…”

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confidence: 99%

“…We apply the numerical integration of the initial system (6)- (8) and check the constraint equation f 0 (1−2N )T N −1 − 1 = 0 at each step of the integration. It should be noted that we can use (10) to decrease the number of degrees of freedom.…”

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confidence: 99%

On Kasner solution in Bianchi I f(T) cosmology

Skugoreva

Toporensky

2018

Eur. Phys. J. C

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Recently the cosmological dynamics of an anisotropic Universe in f (T ) gravity became an area of intense investigations. Some earlier papers devoted to this issue contain contradictory claims about the nature and propertied of vacuum solutions in this theory. The goal of the present paper is to clarify this situation. We compare properties of f (T ) and f (R) vacuum solutions and outline differences between them. The Kasner solution appears to be an exact solution for the T = 0 branch, and an asymptotic solution for the T = 0 branch. It is shown that the Kasner solution is a past attractor if T < 0, being a past and future attractor for the T > 0 branch.The Kasner solution, being one of the first known exact solutions in relativistic cosmology [1] continues to be one of the most important exact solutions in general relativity (GR) or its modifications. One of the reasons is that despite this being a vacuum solution, it is a good approximation near a cosmological singularity for almost all matter sources (except for a stiff fluid) in a flat anisotropic Universe. Moreover, a general cosmological singularity is believed to be constructed as an infinite series of consecutive epochs, each of them being a particular Kasner solution with a good accuracy (though a mathematical proof of this scenario is still absent in full details; see, for example, [2])-the famous BelinskiiKhalatnikov-Lifshitz (BKL) scenario [3]. Therefore the Kasner set of solutions provides "building blocks" for the BKL picture.If we assume that GR needs some modifications at UV scale, it is natural to expect that such modifications should change the behavior near a cosmological singularity significantly. That is why the fate of the Kasner solution in modified gravity theories is an area of intense investigations. A lot of efforts have been devoted to Kasner solutions and their modifications in quadratic gravity. We remind the reader that the Kasner solution is a solution for an anisotropically expanda e-mail: masha-sk@mail.ru b e-mail: atopor@rambler.ru ing Universe with scale factors changing as powers of time. These power exponents are subject of two conditions giving us their sum as well as the sum of their squares (both sums are equal to unity). In quadratic gravity, two different situations were identified:• If the equations of motion are of the second order, as in GR (that is, in Gauss-Bonnet gravity), the power-law solution for the scale factor is an asymptotic solution.In the high-curvature regime, these two conditions for power exponents are different from those in the GR Kasner solution [4][5][6], while the GR Kasner solution is an asymptotic solution in the low-curvature regime.• In fourth order gravity (like R + R 2 or a general quadratic gravity) the Kasner solution (with the same conditions for the exponents) is an exact vacuum solution. However, since the phase space has two additional dimensions in comparison with GR, a Kasner solution in quadratic gravity may be in some situations unstable [7,8].Recently a new class of mod...

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Phase equilibrium and microstructure of topological AdS black holes in massive gravity *

Liu

Du²,

Zhao

et al. 2022

Chinese Phys. C

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In order to clearly understand the gravitational theory through the thermal properties of the black hole, it becomes significant to further investigate the first-order phase transition of black holes. In this paper, we adopt different conjugate variables ($P\sim V$, $T\sim S$, $C_1\sim c_1$, and $C_2\sim c_2$) and apply Maxwell's equal-area law to study the phase equilibrium of topological black hole in massive gravity. The condition and latent heat of phase transition are displayed as well as the coexistent curve of $P-T$. The result shows that the phase transition of this system is the high/low electric potentials one, not only the large/small black holes one. We also analyze the effect of the model's parameters on phase transition. Furthermore we introduce a new order parameter to probe the microstructure of this system. This work will provide the theoretical basis to study the phase structure of topological black holes in massive gravity and to further explore into the gravitational theory. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

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On stability of the Kasner solution in quadratic gravity

Cited by 14 publications

References 42 publications

Beyond the linear analysis of stability in higher derivative gravity with the Bianchi-I metric

Beyond the linear analysis of stability in higher derivative gravity with the Bianchi-I metric

On Kasner solution in Bianchi I f(T) cosmology

Phase equilibrium and microstructure of topological AdS black holes in massive gravity *

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