Astronomy and Astrophysics – Astrophysics
Scientific paper
Apr 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002aps..apri12007h&link_type=abstract
American Physical Society, April Meeting, Jointly Sponsored with the High Energy Astrophysics Division (HEAD) of the American As
Astronomy and Astrophysics
Astrophysics
Scientific paper
We find solutions to Einstein’s equations, generalized to 4+1 dimensions, in which the spatial slices possess anisotropic, Bianchi-type II geometries. We examine these solutions within the context of induced matter theory, a Kaluza-Klein approach developed by Paul S. Wesson teWesson. In this theory, relaxing the assumption that the fifth coordinate is compact leads to extra terms in the field equations. Moved to the stress-energy tensor side of the equations, these terms are identified as ``induced matter’’ components. Of the two sets of solutions we find, one resembles a higher dimensional generalization of Taub’s 3+1 dimensional Bianchi type II solution teTaub. The other set’s scale factors behave in the monotonic manner of the generalized Kasner solution teHalpern, albeit with different parametric relationships. We determine the pressure and density of the induced matter, examining how these evolve over time, and show how natural assumptions lead to the contraction of the fifth scale factor. Finally we comment on the implications of these results for higher dimensional anisotropic models in general. 9 Wesson P.S. Wesson, Space-Time-Matter: Modern Kaluza-Klein Theory, World Scientific, River Edge, NJ (1999). Taub A.H. Taub, Ann. Math. 53 (1951), 472—490. Halpern P. Halpern, Phys. Rev. D63 (2001), 024009. thebibliography
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