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Title: Flat deformation theorem and symmetries in spacetime
Author: Llosa, Josep
Carot, Jaume
Keywords: Relativitat especial (Física)
Special relativity (Physics)
Issue Date: 17-Feb-2009
Publisher: Institute of Physics (IOP)
Abstract: The 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.
Note: Versió postprint del document publicat a:
It is part of: Classical and Quantum Gravity, 2009, vol. 26, num. 5, p. 055013-055032
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ISSN: 0264-9381
Appears in Collections:Articles publicats en revistes (Física Quàntica i Astrofísica)

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