Segre decomposition of spacetimes

Following a recent work in which it is shown that a spacetime admitting Lie -group actions may be disjointly decomposed into a closed subset with no in terior plus a dense finite union of open sets in each of which the characte r 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 (a nd hence of the Einstein tensor) into the decomposition. We also show how t his type of decomposition can be carried out for any type of property of th e spacetime depending on the existence of a continuous endomorphism.