Global dynamics of the Hořava–Lifshitz cosmological system

Gao, Fabao; Llibre, Jaume

doi:10.1007/s10714-019-2635-x

Cited by 8 publications

(16 citation statements)

References 15 publications

(21 reference statements)

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“…Our study will fully describes the global dynamics of system (7) in the region G = (x, z, s) ∈ R 3 : x 2 − z 2 ≤ 1 of physical interest adding its boundary at infinity. It should be noted from the derivation of system (7) that the space curvature k is implicit in the variables x and z.…”

Section: The Cosmological Equationsmentioning

confidence: 99%

“…In order to study the local phase portraits of the finite and infinite equilibrium points, and the global phase portraits of system (7) in the region G, which is the meaningful region for cosmology, see again [4] or [14]. We start discussing the phase portraits on its invariant planes and surface…”

Section: Phase Portraits On the Invariant Planes And Surfacementioning

confidence: 99%

“…In recent years Hořava [1] proposed a spacetime asymmetric gravitational theory similar to Lifshitz's scalar field theory, also known as Hořava-Lifshitz gravity. This theory has inspired a great deal of research for its applications in cosmology and black hole physics (see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] or the review articles [19,20] and the references therein).…”

Section: Introductionmentioning

confidence: 99%

“…With or without detailed-balance condition, few researchers have published several papers on Hořava-Lifshitz gravity through phase space analysis, see for instance [3][4][5][6][7]17]. Among these papers there are also some of them about the case of non-zero space curvature k. When the terms related to k are dominant, Friedmann solution will be generated.…”

Section: Introductionmentioning

confidence: 99%

“…More precisely, they either studied the global dynamics of the planar case of Hořava-Lifshitz gravity with exponential potential by using the twodimensional Poincaré compactification, or discussed only local dynamics of this cosmological model with powerlaw potential but without investigate the dynamics close to infinity. The three-dimensional global dynamics of Hořavaa e-mail: gaofabao@sina.com (corresponding author) b e-mail: jllibre@mat.uab.cat Lifshitz cosmology with k = 0 and = 0 was studied in [7].…”

Section: Introductionmentioning

confidence: 99%

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Global dynamics of Hořava–Lifshitz cosmology with non-zero curvature and a wide range of potentials

Gao

Llibre

2020

Eur. Phys. J. C

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Section: The Cosmological Equationsmentioning

confidence: 99%

Section: Phase Portraits On the Invariant Planes And Surfacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Global dynamics of Hořava–Lifshitz cosmology with non-zero curvature and a wide range of potentials

Gao

Llibre

2020

Eur. Phys. J. C

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Global dynamics of the Hořava–Lifshitz cosmology in the presence of non-zero cosmological constant in a flat space

Gao

Llibre²

2022

Physics of the Dark Universe

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Propagation of a scalar field with non-minimal coupling in three dimensions: Hawking radiation and quasinormal modes

Yekta¹,

Shariat²

2019

Class. Quantum Grav.

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In this paper we investigate an exact spectrum of quasi normal modes (QNMs) for perturbations of a scalar field coupled non-minimally with the Einstein tensor of an uncharged, non-rotating Banados, Teitelboim, and Zanelli (BTZ) black hole in three-dimensional spacetime. Due to the geometry around the black hole, the scalar field encounters an effective potential barrier. We study this potential numerically and derive exact numerical results for the greybody factors (GFs) and discuss their profiles in terms of the coupling constant and black hole parameters. We then proceed to derive the Hawking radiation spectrum for BTZ black hole. 1 d.mahdavian@hsu.ac.ir arXiv:1810.08991v2 [hep-th] 29 Aug 2019Recently it has been devoted a lot of studies of gravitational theories to modification of Einstein's gravity.One class of these theories concern the scalar-tensor theories, such as Horndeski theory which gives a second order field equations in four dimensions [1][2][3]. The Lagrangian of this model contains a term for coupling of a scalar field with curvature tensors. This kind of coupling has interesting cosmological implications [4][5][6][7]. The coupling of the scalar field to Einstein tensor can be regarded effectively as a cosmological constant [6]. On the other hand, this scalar-tensor concept is also intriguing in threedimensional general relativity (GR). Vanishing Newtonian potential in three-dimensional GR disqualifies it to serve as a compatible theory for three-dimensional gravity while the proper description is obtained by dimensional reduction of four-dimensional GR to a scalar-tensor theory in three dimensions. The other standard approach which we will not discuss it here is the addition of higher derivative corrections to GR to produce massive gravity theories in three dimensions proposed in Refs. [8][9][10][11][12]. The nice feature of these theories is that there are different kinds of black hole solutions to their equations of motion [13]-[21], however the most reputed asymptotically AdS one is the BTZ black hole [22]. Within the framework of this theory, the existence of black holes is anticipated, which is an appropriate ground for understanding many aspects of gravity theory.The stability of a black hole can be examined by the study of dynamical behaviors of the perturbations in its background spacetime. The natural vibrational modes of these perturbations in the spacetime exterior to an event horizon are called quasi normal modes (QNMs). The corresponding frequency

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Global dynamics of the Hořava–Lifshitz cosmological system

Abstract: Using the qualitative theory, the global dynamics of the cosmological model based on Hořava-Lifshitz gravity is described.

Cited by 8 publications

References 15 publications

Global dynamics of Hořava–Lifshitz cosmology with non-zero curvature and a wide range of potentials

Global dynamics of Hořava–Lifshitz cosmology with non-zero curvature and a wide range of potentials

Global dynamics of the Hořava–Lifshitz cosmology in the presence of non-zero cosmological constant in a flat space

Propagation of a scalar field with non-minimal coupling in three dimensions: Hawking radiation and quasinormal modes

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