Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1

Details Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1 Essential Constants for Spatially Homogeneous Ricci-flat manifolds of dimension 4+1

2003-11-07

arxiv.org/abs/gr-qc/0311025v2

J.Phys.A37:4039-4058,2004

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 Pages, 2 Tables, latex2e

Scientific paper

10.1088/0305-4470/37/13/008

The present work considers (4+1)-dimensional spatially homogeneous vacuum cosmological models. Exact solutions -- some already existing in the literature, and others believed to be new -- are exhibited. Some of them are the most general for the corresponding Lie group with which each homogeneous slice is endowed, and some others are quite general. The characterization ``general'' is given based on the counting of the essential constants, the line-element of each model must contain; indeed, this is the basic contribution of the work. We give two different ways of calculating the number of essential constants for the simply transitive spatially homogeneous (4+1)-dimensional models. The first uses the initial value theorem; the second uses, through Peano's theorem, the so-called time-dependent automorphism inducing diffeomorphisms

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