Abstract
Two vacuum solutions of 5 dimensional vacuum Einstein’s Equations are obtained assuming only homogeneity and isotropy in the usual 3 space dimensions and general dependence of the metric on time t, as well as on the 5th coordinate ⍦.
Such solutions are shown to exibit always a killing vector field in the t,⍦ submanifold as a consequence of the field equations. This justifies the usual assumption that the geometry of the 5th coordinate is a circle. It is shown they are equivalent to the Lorenz - Petzold type (ix) solutions.
On leave from the Fac. Science of the University of Coimbra.
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© 1988 Kluwer Academic Publishers
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Macedo, P. (1988). Constraints on the Geometry of the 5th dimension in cosmological solutions of Five dimensional Relativity in vacuum. In: Galeotti, P., Schramm, D.N. (eds) Gauge Theory and the Early Universe. NATO ASI Series, vol 248. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3059-9_16
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DOI: https://doi.org/10.1007/978-94-009-3059-9_16
Publisher Name: Springer, Dordrecht
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