Segre decomposition of spacetimes

Abstract

Following a recent work in which it is shown that a spacetime admitting Lie-group actions may be disjointly decomposed into a a closed subset with no interior plus a dense finite union of open sets in each of which the character and dimension of the group orbits as well as the Petrov type are constant, the aim of this work is to include the Segre types of the Ricci tensor (and hence of the Einstein tensor) into the decomposition. We also show how this type of decomposition can be carried out for any type of property of the spacetime depending on the existence of a continuous endomorphism.

15 pages, provisionally scheduled for April 1999 in Class. Quantum Grav

References in corpus (6)

• Stationary and Axisymmetric Perfect-Fluid Solutions with Conformal Motion
• Space-times admitting a three-dimensional conformal group
• G_2 Perfect-Fluid Cosmologies with a proper conformal Killing vector
• Limits of the energy-momentum tensor in general relativity
• Stationary generalized Kerr-Schild spacetimes
• Stationary and Axisymmetric Perfect Fluids with one Conformal Killing Vector

Cited by in corpus (6)

• Uniqueness properties of the Kerr metric
• General study and basic properties of causal symmetries
• Causal symmetries
• Algebraic classification of the gravitational field in Weyl-Cartan space-times
• Segre embedding and related maps and immersions in differential geometry
• Algebraic classification of the gravitational field in general metric-affine geometries