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from Part I - Elements of differential geometry
Published online by Cambridge University Press: 30 May 2024
The Bianchi classification of 3-dimensional Lie algebras is introduced by the Schucking method: mapping the structure constants of the algebras into the set of 3×3 matrices, and then considering all the inequivalent combinations of eigenvalues and eigenvectors. A general 4-dimensional metric with a symmetry algebra of Bianchi type is derived. The general metric of a spatially homogeneous and isotropic (= Robertson–Walker, R–W) spacetime is derived. The possible Bianchi types of R–W spacetimes are demonstrated.
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