Multiply-warped product metrics and reduction of Einstein equations

Gholami, F.; Darabi, F.; Haji‐Badali, Ali

doi:10.1142/s0219887817500219

Cited by 9 publications

(8 citation statements)

References 11 publications

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“…In 2016, D. Dumitru [12], calculated warping functions for multiply generalized Robertson-Walker spacetime to be an Einstein manifold when all fibers are Ricci flat. In 2017, F. Gholami, F. Darabi and A. Haji-Badali [13] studied multiply warped product metrics and reduced Einstein equation for generalized Friedmann-Robrtson-Walker spacetime.…”

Section: Buddhadev Pal and Pankaj Kumarmentioning

confidence: 99%

A family of multiply warped product semi-Riemannian Einstein metrics

Pal¹,

Kumar²

2020

Journal of Geometric Mechanics

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In this paper, we characterize multiply warped product semi -Riemannian manifolds when the base is conformal to an n-dimensional pseudo-Euclidean space. We prove some conditions on warped product semi-Riemannian manifolds to be an Einstein manifold which is invariant under the action of an (n − 1)-dimensional translation group. After that we apply this result for the case of Ricci-flat multiply warped product space when the fibers are Ricci-flat. We also discuss the existence of infinitely many Ricci-flat multiply warped product spaces under the same action with null like vector.

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Section: Buddhadev Pal and Pankaj Kumarmentioning

confidence: 99%

A family of multiply warped product semi-Riemannian Einstein metrics

Pal¹,

Kumar²

2020

Journal of Geometric Mechanics

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“…As the final interesting result, we may consider the Einstein equations ḠAB = − Λḡ AB on ( M , ḡ) with cosmological constant Λ and also using the same strategy explained in [19], we can obtain the following equations…”

Section: Dgp Cosmological Modelmentioning

confidence: 99%

“…The 5-dimensional brane world theories like RS [2], [3] and DGP models [4], may be considered as warped product spacetimes. We have already obtained, in the context of warped product spacetimes, the Einstein equations with cosmological constant in arbitrary (m + n)D and (1 + n)D multidimensional spacetime with multiply-warped product metric ( M , ḡ) [19], [20]. In this paper, motivated by the previous works, we consider arbitrary multidimensional brane world metrics of RS and DGP models with a cosmological constant, as warped product spacetimes.…”

Section: Introductionmentioning

confidence: 99%

On Einstein equations with cosmological constant in braneworld models

2021

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In this paper, we investigate the Einstein equations with cosmological constant for Randall-Sundrum (RS) and Dvali-Gabadadze-Porrati (DGP) models to determine the warp functions in the context of warp product spacetimes. In RS model, it is shown that Einstein's equation in the bulk is reduced into the brane as a vacuum equation, having vacuum solution, which is not affected by the cosmological constant in the bulk. In DGP model, it is shown that the Einstein's equation in the bulk is reduced into the brane and along the extra dimension, where both equations are affected by the cosmological constant in the bulk. We have solved these equations in DGP model, subject to vanishing cosmological constants on the brane and along extra dimension, and obtained exact solutions for the warp functions. The solutions depend on the typical values of cosmological constant in the bulk as well as the dimension of the brane. So, corresponding to the typical values, some solutions have exponential behaviours which may be set to represent warp inflation on the brane, and some other solutions have oscillating behaviours which may be set to represent warp waves or branes waves along the extra dimension.

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“…. , D k ), called a metric-affine almost multi-product manifold, appears in studies of the curvature and Einstein equations on multiply twisted and multiply warped products, see [10,11,12,13,16,20,35,36], in the theory of webs composed of different foliations, see [1], and Dupin hypersurfaces, (which have a constant number of different principal curvatures), see [9,25]. We define the mixed scalar curvature of (M, g, ∇; D 1 , .…”

Section: Introductionmentioning

confidence: 99%

The Mixed Scalar Curvature of Almost-Product Metric-Affine Manifolds

Rovenski

Zawadzki

2018

Results Math

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A pseudo-Riemannian manifold endowed with k > 2 orthogonal complementary distributions (called a Riemannian almost multi-product structure) appears in such topics as multiply warped products, the webs composed of several foliations, Dupin hypersurfaces and in studies of the curvature and Einstein equations. In this article, we consider the following two problems on the mixed scalar curvature of a Riemannian almost multi-product manifold with a linear connection: a) integral formulas and applications to splitting of manifolds, b) variation formulas and applications to the mixed Einstein-Hilbert action, and we generalize certain results on the mixed scalar curvature of pseudo-Riemannian almost product manifolds.

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Multiply-warped product metrics and reduction of Einstein equations

Cited by 9 publications

References 11 publications

A family of multiply warped product semi-Riemannian Einstein metrics

A family of multiply warped product semi-Riemannian Einstein metrics

On Einstein equations with cosmological constant in braneworld models

The Mixed Scalar Curvature of Almost-Product Metric-Affine Manifolds

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