Abstract:
The D-dimensional cosmological model on the manifold M=R×M1×⋯×Mn, describing the evolution of Einstein factor spaces Mi in the presence of a multicomponent perfect fluid source, is considered. The barotropic equation of state for the mass?energy densities and pressures of the components is assumed in each space. Where the number of non-Ricci-flat factor spaces and the number of perfect fluid components are both equal to two, the Einstein equations for the model are reduced to the generalized Emden–Fowler (second-order ordinary differential) equation, which has been recently investigated by Zaitsev and Polyanin using discrete-group analysis. We generate new integrable cosmological models using the integrable classes of this equation and present the corresponding metrics. The method is demonstrated for the special model with Ricci-flat spaces M1 and M2 and a two-component perfect fluid source
Citation:
V. R. Gavrilov, V. N. Melnikov, “Integration of D-dimensional cosmological models with two factor spaces by reduction to the generalized Emden–Fowler equation”, TMF, 114:3 (1998), 454–469; Theoret. and Math. Phys., 114:3 (1998), 355–367
\Bibitem{GavMel98}
\by V.~R.~Gavrilov, V.~N.~Melnikov
\paper Integration of $D$-dimensional cosmological models with two factor spaces by reduction to the generalized Emden--Fowler equation
\jour TMF
\yr 1998
\vol 114
\issue 3
\pages 454--469
\mathnet{http://mi.mathnet.ru/tmf852}
\crossref{https://doi.org/10.4213/tmf852}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1840311}
\zmath{https://zbmath.org/?q=an:0954.83017}
\transl
\jour Theoret. and Math. Phys.
\yr 1998
\vol 114
\issue 3
\pages 355--367
\crossref{https://doi.org/10.1007/BF02575448}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000075184200010}
Linking options:
https://www.mathnet.ru/eng/tmf852
https://doi.org/10.4213/tmf852
https://www.mathnet.ru/eng/tmf/v114/i3/p454
This publication is cited in the following 16 articles:
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Canfora F., Dimakis N., Giacomini A., Paliathanasis A., “Bianchi Ix Cosmologies in the Einstein-Skyrme System in a Sector With Nontrivial Topological Charge”, Phys. Rev. D, 99:4 (2019), 044035
Dimakis N., Terzis P.A., Christodoulakis T., “Integrability of Geodesic Motions in Curved Manifolds Through Nonlocal Conserved Charges”, Phys. Rev. D, 99:10 (2019), 104061
Melnikov V.N., “Multidimensional Cosmology, Constants and Transition To New Si Units”, Internat J Modern Phys A, 26:22 (2011), 3788–3800
V. N. MELNIKOV, “MULTIDIMENSIONAL COSMOLOGY, CONSTANTS AND TRANSITION TO NEW SI UNITS”, Int. J. Mod. Phys. Conf. Ser., 03 (2011), 170
Melnikov V.N., “Multidimensional models, dark energy and fundamental constants”, Astrophysics and Cosmology After Gamow, AIP Conference Proceedings, 1206, 2009, 27–47
Melnikov, VN, “2-component integrable cosmological models”, International Journal of Modern Physics A, 20:11 (2005), 2246
Alimi, JM, “A multicomponent perfect fluid with variable parameters in n Ricci-flat spaces”, Journal of the Korean Physical Society, 45 (2004), S148
Melnikov V.N., Gavrilov V.R., “2-component cosmological models with perfect fluid and scalar field: Exact solutions”, Gravitational Constant: Generalized Gravitational Theories and Experiments, Nato Science Series, Series II: Mathematics, Physics and Chemistry, 141, 2004, 247–268
V. N. Melnikov, V. R. Gavrilov, The Gravitational Constant: Generalized Gravitational Theories and Experiments, 2004, 247
Grebeniuk M.A., Melnikov V.N., “Multidimensional gravity and cosmology and problems of G”, Gravitation and Cosmology: From the Hubble Radius To the Planck Scale, Fundamental Theories of Physics, 126, 2002, 313–320
V. R. Gavrilov, V. N. Melnikov, “D-dimensional p-brane cosmological models associated with a Lie algebra of the type Am”, Theoret. and Math. Phys., 123:3 (2000), 726–743
Goenner, H, “Exact solutions of the generalized Lane-Emden equation”, Journal of Mathematical Physics, 41:10 (2000), 7029
Ivashchuk V.D., Melnikov V.N., “Multidimensional cosmological and spherically symmetric solutions with intersecting p-branes”, Mathematical and Quantum Aspects of Relativity and Cosmology, Lecture Notes in Physics, 536, 2000, 214–247
V D Ivashchuk, V N Melnikov, “Toda
p
-brane black holes and polynomials related to Lie algebras”, Class. Quantum Grav., 17:10 (2000), 2073
Melnikov, VN, “Multidimensional gravity and cosmology”, Journal of the Korean Physical Society, 35 (1999), S675
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