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http://hdl.handle.net/2445/171250
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: https://doi.org/10.1088/0264-9381/26/5/055013 |
It is part of: | Classical and Quantum Gravity, 2009, vol. 26, num. 5, p. 055013-055032 |
URI: | http://hdl.handle.net/2445/171250 |
Related resource: | https://doi.org/10.1088/0264-9381/26/5/055013 |
ISSN: | 0264-9381 |
Appears in Collections: | Articles publicats en revistes (Física Quàntica i Astrofísica) |
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