Decompositions of spacetimes admitting symmetries

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Abstract
It is shown that a spacetime admitting symmetries may be disjointly decomposed into an open dense finite union of open sets in each of which the type (spacelike, timelike or null) and dimension of the symmetry orbits and the Petrov type of the Weyl tensor are constant, together with a closed non-empty subset of M which has no interior. It is also shown that if the symmetries admitted are affine (including Killing and homothetic), conformal or projective, the subset of points of M at which the orbit dimension is maximum is open and dense (i.e. `almost everywhere') in M.

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