Llosa, JosepCarot, Jaume2020-10-152020-10-152009-02-170264-9381https://hdl.handle.net/2445/171250The flat deformation theorem states that given a semi-Riemannian analytic metric g on a manifold, locally there always exists a two-form F, a scalar function c, and an arbitrarily prescribed scalar constraint depending on the point x of the manifold and on F and c, say (c,F, x) = 0, such that the deformed metric η = cg − F2 is semi-Riemannian and flat. In this paper we first show that the above result implies that every (Lorentzian analytic) metric g may bewritten in the extendedKerr-Schild form, namely ηab := agab−2bk(a lb) where η is flat and ka, la are two null covectors such that kala = −1; next we show how the symmetries of g are connected to those of η, more precisely; we show that if the original metric g admits a conformal Killing vector (including Killing vectors and homotheties), then the deformation may be carried out in a way such that the flat deformed metric η 'inherits' that symmetry.21 p.application/pdfeng(c) Institute of Physics (IOP), 2009Relativitat especial (Física)Special relativity (Physics)info:eu-repo/semantics/article6024532020-10-15info:eu-repo/semantics/openAccess