Composite S-Brane Solutions on the Product of Ricci-Flat Spaces

Ivashchuk, V. D.; Melnikov, V. N.; Selivanov, A. B.

doi:10.1023/b:gerg.0000032151.75335.14

Cited by 12 publications

(14 citation statements)

References 47 publications

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“…. ., in [61,62]. It was also confirmed by special black-hole "block-orthogonal" solutions considered earlier in [19,66].…”

Section: Multidimensional Modelssupporting

confidence: 66%

“…In [49], the reduction of p-brane cosmological type solutions to Toda-like systems was first performed. General classes of p-brane solutions (cosmological and spherically symmetric ones) related to Euclidean Toda lattices associated with Lie algebras (mainly A m , C m ones) were obtained in [58][59][60][61][62].…”

Section: Multidimensional Modelsmentioning

confidence: 99%

“…In [61,62], a family of spherically symmetric solutions was investigated, and a subclass of black-hole (BH) configurations related to Toda-type equations with certain asymptotic conditions was singled out. These BH solutions are governed by functions H s (z) > 0, defined on the interval (0, (2μ) −1 ), where μ > 0 is the extremality parameter, and obey a set of differential equations (equivalent to Toda-type ones) d dz In [61,62,65], the following hypothesis was suggested: the functions H s are polynomials when the intersection rules…”

Section: Multidimensional Modelsmentioning

confidence: 99%

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Centenary of Einstein’s general relativity. Its present extensions

Melnikov

2016

Gravit. Cosmol.

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This paper is a brief review of integrable models of gravitation and cosmology in four and more dimensions which make up one of the proper approaches to studying the basic issues and strong field objects, the early and present Universe, and black hole (BH) physics in particular. The main results within this approach, obtained in the recent years by the research group founded by K.P. Staniukovich, are presented. Absolute G measurements and problems of its possible time and range variations, which are reflections of the unification problem, are discussed within these models. The choice, nature, classification and precision of determination of fundamental physical constants and their role in the expected transition to new definitions of basic SI units, supposed to be based on fundamental physical constants and stable quantum phenomena, are described. A need for further absolute measurements of G, its possible range and time variations is stressed. The multipurpose space project SEE is shortly described, aimed at measuring G and its stability in space and time with a progress of 2-3 orders of magnitude against the present accuracy. It may answer many important questions posed by gravitation, cosmology and unified theories. A project of a laboratory experiment to test possible deviations from Newton's law of gravity is also presented.

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“…. ., in [61,62]. It was also confirmed by special black-hole "block-orthogonal" solutions considered earlier in [19,66].…”

Section: Multidimensional Modelssupporting

confidence: 66%

Section: Multidimensional Modelsmentioning

confidence: 99%

Section: Multidimensional Modelsmentioning

confidence: 99%

See 1 more Smart Citation

Centenary of Einstein’s general relativity. Its present extensions

Melnikov

2016

Gravit. Cosmol.

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“…S-branes were originally space-like analogues of D-branes; see also [53,[96][97][98][99][100][101][102][103] and the references therein.…”

Section: Solutions With Ricci-flat Factor-spacesmentioning

confidence: 99%

On Brane Solutions with Intersection Rules Related to Lie Algebras

Ivashchuk

2017

Symmetry

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Abstract:The review is devoted to exact solutions with hidden symmetries arising in a multidimensional gravitational model containing scalar fields and antisymmetric forms. These solutions are defined on a manifold of the form M = M 0 × M 1 × . . . × M n , where all M i with i ≥ 1 are fixed Einstein (e.g., Ricci-flat) spaces. We consider a warped product metric on M . Here, M 0 is a base manifold, and all scale factors (of the warped product), scalar fields and potentials for monomial forms are functions on M 0 . The monomial forms (of the electric or magnetic type) appear in the so-called composite brane ansatz for fields of forms. Under certain restrictions on branes, the sigma-model approach for the solutions to field equations was derived in earlier publications with V.N.Melnikov. The sigma model is defined on the manifold M 0 of dimension d 0 = 2 . By using the sigma-model approach, several classes of exact solutions, e.g., solutions with harmonic functions, S-brane, black brane and fluxbrane solutions, are obtained. For d 0 = 1 , the solutions are governed by moduli functions that obey Toda-like equations. For certain brane intersections related to Lie algebras of finite rank-non-singular Kac-Moody (KM) algebras-the moduli functions are governed by Toda equations corresponding to these algebras. For finite-dimensional semi-simple Lie algebras, the Toda equations are integrable, and for black brane and fluxbrane configurations, they give rise to polynomial moduli functions. Some examples of solutions, e.g., corresponding to finite dimensional semi-simple Lie algebras, hyperbolic KM algebras: H 2 (q, q) , AE 3 , H A (1) 2 , E 10 and Lorentzian KM algebra P 10 , are presented.

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“…For the plane waves (H = A ij (u)x i x j ), sometime it is useful to rewrite the metric in the Rosen coordinates, g = 2dvdu + h, where h = C ij (u)x i x j is a family of flat metrics, see e.g. [1,15,17]. The examples of the Einstein metrics that we construct have a similar structure.…”

Section: Introductionmentioning

confidence: 99%