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1 results

  • 10 - The spatially homogeneous Bianchi-type spacetimes

  • from Part I - Elements of differential geometry
  • Jerzy Plebanski, National Polytechnic Institute of Mexico, Andrzej Krasinski, Nicolaus Copernicus Astronomical Center, Polish Academy of Sciences
  • Book:
    An Introduction to General Relativity and Cosmology
    Published online:
    30 May 2024
    Print publication:
    06 June 2024, pp 94-107

  • Summary

    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.