Embeddings in space–times sourced by scalar fields

Anderson, Edward; Dahia, F.; Lidsey, James E.; Romero, C.

doi:10.1063/1.1610237

Cited by 22 publications

(38 citation statements)

References 59 publications

(83 reference statements)

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“…This is because due to the presence of the BD scalar field the ambient space is not, in general, Ricci-flat. However, it can be shown that a new geometrical frame for 5D Brans-Dicke theory exists and is supported by an extension of the Campbell-Magaard theorem [14]. On the other hand, as in the case of the induced-matter approach, the theory provides no way of obtaining a unique spacetime from a given 5D metric, and that would require further mathematical conditions on the embedding, or a kind of new dynamical principle to select the possible choices of physically plausible spacetimes [32].…”

Section: Final Remarksmentioning

confidence: 97%

“…The anwer to this question was provided by the Campbell-Magaard theorem, which asserts that any analytic n-dimensional Riemannian space can be locally embedded in a (n + 1)-dimensional Ricci-flat space [8][9][10][11]. The rediscovery of Campbell-Magaard theorem by physicists and its connection with modern spacetime embedding theories gave rise to a series of new results and extensions in the cases when the ambient space: (a) is an Einstein space [12], (b) has a non-degenerate Ricci-tensor [13], (c) is sourced by scalar-fields [14]. The latter case includes embeddings in spaces that are solutions of the vacuum Brans-Dicke (BD) field equations.…”

Section: Introductionmentioning

confidence: 99%

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Modified Brans–Dicke theory of gravity from five-dimensional vacuum

2007

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We investigate, in the context of five-dimensional (5D) Brans-Dicke theory of gravity, the idea that macroscopic matter configurations can be generated from pure vacuum in five dimensions, an approach first proposed by Wesson and collaborators in the framework of 5D general relativity. We show that the 5D Brans-Dicke vacuum equations when reduced to four dimensions (4D) lead to a modified version of Brans-Dicke theory in 4D. As an application of the formalism, we obtain two 5D extensions of 4D O'Hanlon and Tupper vacuum solution and show that they lead two different cosmological scenarios in 4D.

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Section: Final Remarksmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Modified Brans–Dicke theory of gravity from five-dimensional vacuum

2007

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“…For example, in these proposals our ordinary spacetime is viewed as a hypersurface embedded in a five-dimensional (5D) manifold (the bulk). On the other hand, mathematical theorems regulate these embeddings, in particular, the Campbell-Magaard theorem [13,14] and its extensions specify the conditions under which the embeddings are possible [15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Inducing the Cosmological Constant from Five-Dimensional Weyl Space

Aguilar

Romero

2009

Found Phys

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We investigate the possibility of inducing the cosmological constant from extra dimensions by embedding our four-dimensional Riemannian space-time into a five-dimensional Weyl integrable space. Following the approach of the space-timematter theory we show that when we go down from five to four dimensions, the Weyl field may contribute both to the induced energy-tensor as well as to the cosmological constant , or more generally, it may generate a time-dependent cosmological parameter (t). As an application, we construct a simple cosmological model in which (t) has some interesting properties.

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“…Since the nineteenth century, isometric embeddings into higher dimensions have been explored extensively in geometry [1][2][3][4][5][6][7], with more focus on non-Euclidean spaces in recent times. Theorems given by Dahia and Romero [5,6] prove that there exists a local isometric embedding of any analytic pseudo-Riemannian manifold into an Einstein space and also into a more general pseudo-Riemannian space.…”

Section: Introductionmentioning

confidence: 99%

An investigation of embeddings for spherically symmetric spacetimes into Einstein manifolds

Moodley

Amery

2011

Pramana - J Phys

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Embeddings into higher dimensions are very important in the study of higherdimensional theories of our Universe and in high-energy physics. Theorems which have been developed recently guarantee the existence of embeddings of pseudo-Riemannian manifolds into Einstein spaces and more general pseudo-Riemannian spaces. These results provide a technique that can be used to determine solutions for such embeddings. Here we consider local isometric embeddings of four-dimensional spherically symmetric spacetimes into five-dimensional Einstein manifolds. Difficulties in solving the five-dimensional equations for given four-dimensional spaces motivate us to investigate embedded spaces that admit bulks of a specific type. We show that the general Schwarzschild-de Sitter spacetime and Einstein Universe are the only spherically symmetric spacetimes that can be embedded into an Einstein space of a particular form, and we discuss their five-dimensional solutions.

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Embeddings in space–times sourced by scalar fields

Cited by 22 publications

References 59 publications

Modified Brans–Dicke theory of gravity from five-dimensional vacuum

Modified Brans–Dicke theory of gravity from five-dimensional vacuum

Inducing the Cosmological Constant from Five-Dimensional Weyl Space

An investigation of embeddings for spherically symmetric spacetimes into Einstein manifolds

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