Flat deformation theorem and symmetries in spacetime
| dc.creator | Llosa, Josep | |
| dc.creator | Carot, Jaume | |
| dc.date | 2008-09-05 | |
| dc.date | 2009-01-09 | |
| dc.date.accessioned | 2026-07-07T12:43:58Z | |
| dc.date.available | 2026-07-07T12:43:58Z | |
| dc.description | The \emph{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 $Ψ(c, F, x)=0$, such that the \emph{deformed metric} $η= cg -εF^2$ is semi-Riemannian and flat. In this paper we first show that the above result implies that every (Lorentzian analytic) metric $g$ may be written in the \emph{extended Kerr-Schild form}, namely $η_{ab} := a g_{ab} - 2 b k_{(a} l_{b)}$ where $η$ is flat and $k_a, l_a$ are two null covectors such that $k_a l^a= -1$; 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. | |
| dc.description | 30 pages, 0 figures | |
| dc.identifier | https://arxiv.org/abs/0809.1030 | |
| dc.identifier | http://arxiv.org/abs/0809.1030 | |
| dc.identifier | Class.Quant.Grav.26:055013,2009 | |
| dc.identifier | doi:10.1088/0264-9381/26/5/055013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/220605 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Flat deformation theorem and symmetries in spacetime | |
| dc.type | text |