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Power-Law Type Solutions of Fourth-Order Gravity

Please always quote using this URN: urn:nbn:de:0297-zib-466
  • We study the power-law type solutions of the fourth order field equations derived from a generic quadratic Lagrangian density in the case of multidimensional Bianchi I cosmological models. All the solutions of the system of algebraic equations have been found, using computer algebra, from a search of the Groebner bases associated to it. While, in space dimension $ d = 3 $ , the Einsteinian Kasner metric is still the most general power-law type solution, for $ d > 3 $ , no solution, other than the Minkowski space-time, is common to the three systems of equations associated with the three contributions to the Lagrangian density. In the case of a pure Riemann-squared contribution (suggested by a recent calculation of the effective action for the heterotic string), the possibility exists to realize a splitting of the $ d $-dimensional space into a ( $ d - 3 $)-dimensional internal space and a physical 3- dimensional space, the latter expanding in time as a power bigger than 2 (about 4.5 when $ d = 9 $).

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Metadaten
Author:H. Caprasse, J. Demaret, Karin Gatermann, Herbert Melenk
Document Type:ZIB-Report
Date of first Publication:1990/12/11
Series (Serial Number):ZIB-Report (SC-90-18)
ZIB-Reportnumber:SC-90-18
Published in:Appeared in: International Journal of Modern Physics C, Vol. 2, No. 2 (1991), pp. 601-611
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