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TMF, 2000, Volume 123, Number 3, Pages 374–394 (Mi tmf610)  

This article is cited in 12 scientific papers (total in 12 papers)

$D$-dimensional $p$-brane cosmological models associated with a Lie algebra of the type $A_m$

V. R. Gavrilov, V. N. Melnikov

Russian Research Institute for Metrological Service

Abstract: We study a $D$-dimensional cosmological model on the manifold $\mathbf M= \mathbb R\times M_0\times\cdots\times M_n$ describing an evolution of $n+1$ Einstein factor spaces $M_i$ in a theory with several dilatonic scalar fields and differential forms admitting an interpretation in terms of intersecting $p$-branes. The equations of motion of the model are reduced to the Euler–Lagrange equations for the so-called pseudo-Euclidean Toda-like system. Assuming that the characteristic vectors related to the configuration of $p$-branes and their couplings to the dilatonic scalar fields can be interpreted as the root vectors of a Lie algebra of the type $A_m\equiv sl(m+1,\mathbb C)$, we reduce the model to an open Toda chain, which is integrable by the customary methods. The resulting metric has the form of the Kasner solution. We single out the particular model describing the Friedman-like evolution of the three-dimensional external factor space $M_0$ e Einsteinian conformal gaugeraction of the internal factor spaces $M_1,…,M_n$.


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English version:
Theoretical and Mathematical Physics, 2000, 123:3, 726–743

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Received: 25.05.1999
Revised: 05.11.1999

Citation: V. R. Gavrilov, V. N. Melnikov, “$D$-dimensional $p$-brane cosmological models associated with a Lie algebra of the type $A_m$”, TMF, 123:3 (2000), 374–394; Theoret. and Math. Phys., 123:3 (2000), 726–743

Citation in format AMSBIB
\by V.~R.~Gavrilov, V.~N.~Melnikov
\paper $D$-dimensional $p$-brane cosmological models associated with a Lie algebra of the type $A_m$
\jour TMF
\yr 2000
\vol 123
\issue 3
\pages 374--394
\jour Theoret. and Math. Phys.
\yr 2000
\vol 123
\issue 3
\pages 726--743

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    This publication is cited in the following articles:
    1. Ivashchuk, VD, “Exact solutions in multidimensional gravity with antisymmetric forms”, Classical and Quantum Gravity, 18:20 (2001), R87  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. Ivashchuk V.D., Melnikov V.N., “Exact solutions in multidimensional gravity with p-branes and PPN parameters”, Exact Solutions and Scalar Fields in Gravity: Recent Developments, 2001, 123–132  adsnasa  isi
    3. Ivashchuk, VD, “Composite fluxbranes with general intersections”, Classical and Quantum Gravity, 19:11 (2002), 3033  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. Ivashchuk, VD, “Composite S-brane solutions related to Toda-type systems”, Classical and Quantum Gravity, 20:2 (2003), 261  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. Melnikov V.N., “P-branes, extra dimensions and their observational windows”, Cosmology and Gravitation, AIP Conference Proceedings, 668, 2003, 187–197  crossref  zmath  adsnasa  isi
    6. Melnikov V.N., “Gravity and cosmology as key problems of the millennium”, Albert Einstein Century International Conference, AIP Conference Proceedings, 861, 2006, 109–126  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. Melnikov V.N., “Integrable cosmological models in DD and variations of fundamental constants”, Gravitation and Astrophysics: on the Occasion of the 90th Year of General Relativity, 2007, 53–68  crossref  adsnasa  isi
    8. Ivashchuk V.D., Melnikov V.N., “Multidimensional gravitational models: fluxbrane and S-brane solutions with polynomials”, Cosmology and Gravitation, AIP Conference Proceedings, 910, 2007, 411–421  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    9. Melnikov, VN, “MULTIDIMENSIONAL COSMOLOGY AND FUNDAMENTAL CONSTANTS”, International Journal of Modern Physics A, 24:8–9 (2009), 1473  crossref  mathscinet  zmath  adsnasa  isi
    10. Vladimir D. Ivashchuk, Vitaly N. Melnikov, “On Brane Solutions Related to Non-Singular Kac–Moody Algebras”, SIGMA, 5 (2009), 070, 34 pp.  mathnet  crossref  mathscinet
    11. Melnikov V.N., “Centenary of Einstein?s general relativity. Its present extensions”, Gravit. Cosmol., 22:2 (2016), 80–96  crossref  mathscinet  zmath  isi  scopus
    12. Ivashchuk V.D., “On Brane Solutions With Intersection Rules Related to Lie Algebras”, Symmetry-Basel, 9:8 (2017), 155  crossref  mathscinet  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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