Flat deformation theorem and symmetries in spacetime
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 de...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2009 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/171250 |
| Acceso en línea: | https://hdl.handle.net/2445/171250 |
| Access Level: | acceso abierto |
| Palabra clave: | Relativitat especial (Física) Special relativity (Physics) |
| Sumario: | 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. |
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