Multidimensional integrable vacuum cosmology with two curvatures

Gavrilov, V. R.; Ivashchuk, V. D.; Melnikov, V. N.

doi:10.1088/0264-9381/13/11/018

Cited by 31 publications

(31 citation statements)

References 27 publications

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“…We have shown that this result is compatible with the exact 1 + 3 + 6 solution from Ref. [54]. (Recall that only three exact solutions are known for a vacuum cosmological model with a product of two Einstein spaces, see Ref.…”

Section: óò ðù× óò×supporting

confidence: 84%

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Models of G time variations in diverse dimensions

Melnikov

2009

Front. Phys. China

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A review of different cosmological models in diverse dimensions leading to a relatively small time variation of the effective gravitational constant G is presented. Among them: 4-dimensional general scalar-tensor model, multidimensional vacuum model with two curved Einstein spaces, multidimensional model with multicomponent anisotropic "perfect fluid", S-brane model with scalar fields and two form field etc. It is shown that there exist different possible ways of explanation of relatively small time variation of the effective gravitational constant G compatible with present cosmological data (e.g. acceleration): 4-dimensional scalar-tensor theories or multidimensional cosmological models with different matter sources. The experimental bounds on G-dot may be satisfied ether in some restricted interval or for all allowed values of the synchronous time variable.Comment: 27 pages, Late

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Section: óò ðù× óò×supporting

confidence: 84%

“…(Recall that only three exact solutions are known for a vacuum cosmological model with a product of two Einstein spaces, see Ref. [54]. ) We also presented another example where two factor spaces are Ricci-flat and for a two-component example (dust + 5-brane) we obtained a small enough variation of G.…”

Section: óò ðù× óò×mentioning

confidence: 96%

Models of G time variations in diverse dimensions

Melnikov

2009

Front. Phys. China

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“…For the two component perfect-fluid there were solutions with two curvatures, i.e. n = 2, (3,6), (5,5) [106] and corresponding non-singular solutions from [141]. Among the solutions [106] there exists a special class of Milne-type solutions.…”

Section: Multidimensional Modelsmentioning

confidence: 99%

“…n = 2, (3,6), (5,5) [106] and corresponding non-singular solutions from [141]. Among the solutions [106] there exists a special class of Milne-type solutions. Recently some interesting extensions of 2-component solutions were obtained in [107].…”

Section: Multidimensional Modelsmentioning

confidence: 99%

Multidimensional Cosmological and Spherically Symmetric Solutions with Intersecting p-Branes

Ivashchuk

Melnikov

2000

Mathematical and Quantum Aspects of Relativity and Cosmology

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Abstract. Multidimensional model describing the "cosmological" and/ or spherically symmetric configuration with (n + 1) Einstein spaces in the theory with several scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, n "internal" spaces are Ricci-flat, one space M 0 has a non-zero curvature, and all p-branes do not "live" in M 0 , a class of exact solutions is obtained if certain block-orthogonality relations on p-brane vectors are imposed. A subclass of spherically-symmetric solutions containing non-extremal p-brane black holes is considered. Post-Newtonian parameters are calculated and some examples are considered.

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“…Nonlinear ordinary differential equations play a significant role in many physical and technical applications [7,8,16,17,21,27,29,30]. Most of these equations have no analytical solution and numerical techniques may be used to obtain approximate ones.…”

Section: Introductionmentioning

confidence: 99%

On the solutions of a class of nonlinear ordinary differential equations by the Bessel polynomials

Yüzbaşı¹,

Şahı̇n²

2012

Journal of Numerical Mathematics

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In this study, we suggest a collocation method to solve a class of the nonlinear differential equations under the mixed conditions in terms of the Bessel polynomials. The method is based on the matrix forms of the Bessel polynomials and their derivatives by means of collocation points. To illustrate the usefulness of this technique we apply it to some test problems and the comparisons are made with existing results. The results show the efficiently and accuracy of the present work. All of the numerical computations have been performed on computer using a program written in Maple.

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Multidimensional integrable vacuum cosmology with two curvatures

Cited by 31 publications

References 27 publications

Models of G time variations in diverse dimensions

Models of G time variations in diverse dimensions

Multidimensional Cosmological and Spherically Symmetric Solutions with Intersecting p-Branes

On the solutions of a class of nonlinear ordinary differential equations by the Bessel polynomials

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