Classification of 5d warped spaces with cosmological constant

Bejancu, Aurel; Călin, Constantin; Farran, Hani Reda

doi:10.1063/1.4768714

Cited by 8 publications

(7 citation statements)

References 22 publications

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“…We have shown that all vacuum solutions of general relativity in n-dimensions, with or without a cosmological constant Λ (n) , can in several nonequivalent ways be embedded in a (n + 1)-dimensional space which is either an Einstein space or a solution of the higher-dimensional field equations whose source is a real massless scalar field Ψ, minimally-coupled to Einstein gravity and self-interacting through a potential V (Ψ). This work generalizes a number of results discussed in the literature [43][44][45][46][47][48].…”

Section: Final Remarkssupporting

confidence: 85%

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Embeddings for general relativity

León¹

2015

Class. Quantum Grav.

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We present a systematic approach to embed n-dimensional vacuum general relativity in an (n + 1)-dimensional pseudo-Riemannian spacetime whose source is either a (non)zero cosmological constant or a scalar field minimallycoupled to Einstein gravity. Our approach allows us to generalize a number of results discussed in the literature. We construct all the possible (physically distinct) embeddings in Einstein spaces, including the Ricci-flat ones widely discussed in the literature. We examine in detail their generalization, which -in the framework under consideration -are higher-dimensional spacetimes sourced by a scalar field with flat (constant = 0) potential. We use the Kretschmann curvature scalar to show that many embedding spaces have a physical singularity at some finite value of the extra coordinate. We develop several classes of embeddings that are free of singularities, have distinct non-vanishing self-interacting potentials and are continuously connected (in various limits) to Einstein embeddings. We point out that the induced metric possesses scaling symmetry and, as a consequence, the effective physical parameters (e.g., mass, angular momentum, cosmological constant) can be interpreted as functions of the extra coordinate.

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Section: Final Remarkssupporting

confidence: 85%

“…In this paper we present a systematic approach that allows us to tackle all these embeddings in a unified manner in such a way that we (i) reproduce known results, (ii) construct new embeddings and (iii) give concrete answers to the above-mentioned questions. Our results complement and generalize those obtained in [36,[43][44][45][46][47][48].…”

supporting

confidence: 89%

Embeddings for general relativity

León¹

2015

Class. Quantum Grav.

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“…Bejancu et al in Ref. [3], by using the extrinsic curvature of the horizontal distribution, obtained the classification of all spaces ( M , ḡ) satisfying Einstein equations Ḡ = − Λḡ, where ( M , ḡ) is a 5D warped space defined by 4D spacetime (M, g) and the warped function. They described all the exact solutions for the warped metric by means of 4D exact solutions.…”

Section: Introductionmentioning

confidence: 99%

On cosmological constant of generalized Robertson-Walker space-times

Faghfouri

Haji‐Badali

Gholami

2017

Journal of Mathematical Physics

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We study Einstein's equation in (m + n)D and (1 + n)D warped spaces (M ,ḡ) and classify all such spaces satisfying Einstein equationsḠ = −Λḡ. We show that the warping function not only can determine the cosmological constantΛ but also it can determine the cosmological constant Λ appearing in the induced Einstein equations G = −Λh on (M 2 , h). Moreover, we discuss on the origin of the 4D cosmological constant as an emergent effect of higher dimensional warped spaces.

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“…[13]) and to obtain a classification of the warped 5D spaces satisfying Einstein equations with cosmological constant (cf. [14]).…”

Section: Introductionmentioning

confidence: 99%

On Higher Dimensional Kaluza-Klein Theories

Bejancu

2013

Advances in High Energy Physics

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We present a new method for the study of general higher dimensional Kaluza-Klein theories. Our new approach is based on the Riemannian adapted connection and on a theory of adapted tensor fields in the ambient space. We obtain, in a covariant form, the fully general 4D equations of motion in a (4 +n)D general gauge Kaluza-Klein space. This enables us to classify the geodesics of the (4 +n)D space and to show that the induced motions in the 4D space bring more information than motions from both the 4D general relativity and the 4D Lorentz force equations. Finally, we note that all the previous studies on higher dimensional Kaluza-Klein theories are particular cases of the general case considered in the present paper.

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Classification of 5d warped spaces with cosmological constant

Cited by 8 publications

References 22 publications

Embeddings for general relativity

Embeddings for general relativity

On cosmological constant of generalized Robertson-Walker space-times

On Higher Dimensional Kaluza-Klein Theories

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