Cosmology:General Relativity; General Relativity:Cosmology
Abstract :
[en] The exterior calculus package EXCALC2, developed by Schrüfer, is used to implement Siklos' method on a computer. By an appropriate choice of the 1-form basis of spatially homogeneous cosmological models, making use of the time-dependent automorphisms of the Lie algebra, it is possible to obtain a compact form of Einstein's field equations for general models of this type. The explicit expression of the equations, obtained with the help of EXCALC2, is given here for two nondiagonal five-dimensional spatially homogeneous models, namely G[SUB]1[/SUB] and G[SUB]8[/SUB]. These equations constitute an ideal tool for the study of the dynamics of these models: an oscillatory behavior has been found for model G[SUB]1[/SUB], while model G[SUB]8[/SUB] exhibits a monotonous kasnerian mode of approach to the initial singularity.
Disciplines :
Physics
Author, co-author :
De Rop, Yves ; Département de Physique, Facultés universitaires Notre-Dame de la Paix
Demaret, Jacques
Language :
English
Title :
Using EXCALC to study nondiagonal multidimensional spatially homogeneous cosmologies.
Roque W.L., Ellis G.F.R. Axisymmetric Systems, Galaxies and Relativity, M. A. H., MacCallum, Cambridge University Press, Cambridge; 1985.
.
Schrüfer E., Hehl F.W., McCrea J.D. Gen. Rel. Grav. 1987, 19:197.
De Rop Y., Demaret J. (1988) Table of Ricci Tensors for General Non-Diagonal Bianchi Models. Internal publication, University of Namur, Belgium; .
Araujo M.E., Skea J.E.F. 11th International Conference on General Relativity and Gravitation, Stockholm, Abstracts of Contributed Paper 1986, 1:52.
.
Demaret J., Hanquin J.-L. Phys. Rev. D 1985, 31:258.
Halpern P. Phys. Rev. D 1986, 33:354.
Fee G.J. Masters thesis, University of Waterloo, Ontario; 1979.
Demaret J., Hanquin J.-L., Henneaux M., Spindel P., Taormina A. (1986) The fate of the mixmaster behaviour in vacuum inhomogeneous Kaluza-Klein cosmological models. Physics Letters B 175:129.
Jensen L.G. Phys. Lett. B 1987, 192:315.
Taub A.H. (1951) Empty Space-Times Admitting a Three Parameter Group of Motions. The Annals of Mathematics 53:472.
