Cosmological perfect-fluids in f(R) gravity

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

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A note on generalized Robertson–Walker space-times

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887816500791 ◽

2016 ◽

Vol 13 (06) ◽

pp. 1650079 ◽

Cited By ~ 14

Author(s):

Carlo Alberto Mantica ◽

Young Jin Suh ◽

Uday Chand De

Keyword(s):

Vector Field ◽

Scalar Field ◽

Perfect Fluid ◽

Curvature Tensor ◽

Weyl Tensor ◽

Space Time ◽

Stiff Matter ◽

Conformal Curvature ◽

Conformal Curvature Tensor ◽

Mass Less Scalar Field

A generalized Robertson–Walker (GRW) space-time is the generalization of the classical Robertson–Walker space-time. In the present paper, we show that a Ricci simple manifold with vanishing divergence of the conformal curvature tensor admits a proper concircular vector field and it is necessarily a GRW space-time. Further, we show that a stiff matter perfect fluid space-time or a mass-less scalar field with time-like gradient and with divergence-free Weyl tensor are GRW space-times.

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Stress Energy Tensor Study in Fluid Mechanics

10.20944/preprints201903.0061.v1 ◽

2019 ◽

Author(s):

Roman Baudrimont

Keyword(s):

General Relativity ◽

Fluid Mechanics ◽

Space Time ◽

Newtonian Fluids ◽

Third Party ◽

Energy Tensor ◽

Stress Energy Tensor ◽

Perfect Fluids ◽

Stress Energy

This paper is to summarize the involvement of the stress energy tensor in the study of fluid mechanics. In the first part we will see the implication that carries the stress energy tensor in the framework of general relativity. In the second part, we will study the stress energy tensor under the mechanics of perfect fluids, allowing us to lead third party in the case of Newtonian fluids, and in the last part we will see that it is possible to define space-time as a no-Newtonian fluids.

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Cosmological perfect fluids in Gauss–Bonnet gravity

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887819501330 ◽

2019 ◽

Vol 16 (09) ◽

pp. 1950133 ◽

Cited By ~ 20

Author(s):

Salvatore Capozziello ◽

Carlo Alberto Mantica ◽

Luca Guido Molinari

Keyword(s):

Perfect Fluid ◽

Topological Invariant ◽

Energy Tensor ◽

Curvature Scalar ◽

Stress Energy Tensor ◽

Perfect Fluids ◽

Stress Energy ◽

Walker Metric ◽

Friedmann Robertson Walker ◽

Hubble Flow

In a [Formula: see text]-dimensional Friedmann–Robertson–Walker metric, it is rigorously shown that any analytical theory of gravity [Formula: see text], where [Formula: see text] is the curvature scalar and [Formula: see text] is the Gauss–Bonnet topological invariant, can be associated to a perfect-fluid stress–energy tensor. In this perspective, dark components of the cosmological Hubble flow can be geometrically interpreted.

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Pseudo-Z symmetric space-times with divergence-free Weyl tensor and pp-waves

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887816500158 ◽

2016 ◽

Vol 13 (02) ◽

pp. 1650015 ◽

Cited By ~ 9

Author(s):

Carlo Alberto Mantica ◽

Young Jin Suh

Keyword(s):

Symmetric Space ◽

Weyl Tensor ◽

Killing Vector ◽

Complete Classification ◽

Space Time ◽

Conformal Killing ◽

Conformally Flat ◽

Conformal Curvature ◽

Wave Space ◽

Divergence Free

In this paper we present some new results about [Formula: see text]-dimensional pseudo-Z symmetric space-times. First we show that if the tensor Z satisfies the Codazzi condition then its rank is one, the space-time is a quasi-Einstein manifold, and the associated 1-form results to be null and recurrent. In the case in which such covector can be rescaled to a covariantly constant we obtain a Brinkmann-wave. Anyway the metric results to be a subclass of the Kundt metric. Next we investigate pseudo-Z symmetric space-times with harmonic conformal curvature tensor: a complete classification of such spaces is obtained. They are necessarily quasi-Einstein and represent a perfect fluid space-time in the case of time-like associated covector; in the case of null associated covector they represent a pure radiation field. Further if the associated covector is locally a gradient we get a Brinkmann-wave space-time for [Formula: see text] and a pp-wave space-time in [Formula: see text]. In all cases an algebraic classification for the Weyl tensor is provided for [Formula: see text] and higher dimensions. Then conformally flat pseudo-Z symmetric space-times are investigated. In the case of null associated covector the space-time reduces to a plane wave and results to be generalized quasi-Einstein. In the case of time-like associated covector we show that under the condition of divergence-free Weyl tensor the space-time admits a proper concircular vector that can be rescaled to a time like vector of concurrent form and is a conformal Killing vector. A recent result then shows that the metric is necessarily a generalized Robertson–Walker space-time. In particular we show that a conformally flat [Formula: see text], [Formula: see text], space-time is conformal to the Robertson–Walker space-time.

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On the quasi-conformal curvature tensor of an almost Kenmotsu manifold with nullity distributions

Facta Universitatis Series Mathematics and Informatics ◽

10.22190/fumi1802255d ◽

2018 ◽

Vol 33 (2) ◽

pp. 255

Author(s):

Dibakar Dey ◽

Pradip Majhi

Keyword(s):

Vector Field ◽

Curvature Tensor ◽

Conformally Flat ◽

Kenmotsu Manifold ◽

Conformal Curvature ◽

Conformal Curvature Tensor ◽

Kenmotsu Manifolds ◽

Almost Kenmotsu Manifolds ◽

Nullity Distribution ◽

Characteristic Vector Field

The object of the present paper is to characterize quasi-conformally flat and $\xi$-quasi-conformally flat almost Kenmotsu manifolds with $(k,\mu)$-nullity and $(k,\mu)'$-nullity distributions respectively. Also we characterize almost Kenmotsu manifolds with vanishing extended quasi-conformal curvature tensor and extended $\xi$-quasi-conformally flat almost Kenmotsu manifolds such that the characteristic vector field $\xi$ belongs to the $(k,\mu)$-nullity distribution.

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THE RENORMALIZED VACUUM STRESS-ENERGY TENSOR OF de SITTER SPACE-TIME

Acta Physica Sinica ◽

10.7498/aps.33.1759 ◽

1984 ◽

Vol 33 (12) ◽

pp. 1759

Author(s):

YU NAI-CHANG

Keyword(s):

De Sitter Space ◽

Space Time ◽

Energy Tensor ◽

De Sitter ◽

Stress Energy Tensor ◽

Stress Energy

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Cosmological model favored by the holographic principle

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194516601277 ◽

2016 ◽

Vol 41 ◽

pp. 1660127

Author(s):

Irina Dymnikova ◽

Anna Dobosz ◽

Bożena Sołtysek

Keyword(s):

Cosmological Model ◽

Cosmological Constant ◽

Space Time ◽

Holographic Principle ◽

Einstein Equations ◽

Energy Tensor ◽

De Sitter ◽

Quantum Evaporation ◽

Stress Energy ◽

De Sitter Vacua

We present a regular spherically symmetric cosmological model of the Lemaitre class distinguished by the holographic principle as the thermodynamically stable end-point of quantum evaporation of the cosmological horizon. A source term in the Einstein equations connects smoothly two de Sitter vacua with different values of cosmological constant and corresponds to anisotropic vacuum dark fluid defined by symmetry of its stress-energy tensor which is invariant under the radial boosts. Global structure of space-time is the same as for the de Sitter space-time. Cosmological evolution goes from a big initial value of the cosmological constant towards its presently observed value.

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