The kinematical role of automorphisms in the orthonormal frame approach to Bianchi cosmology

Abstract

The automorphism group and frame commutator relations in the orthonormal frame approach to Bianchi cosmology are used to construct an explicit coordinate representation of the orthonormal frame itself (and hence of the spacetime metric) which depends algebraically on the connection coefficients. This is not possible in general inhomogeneous models where differential equations must instead be solved. The shift vector field required for this procedure is intimately related to the true Smarr–York minimal strain and minimal distortion shifts.