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Symmetries of the Einstein Equations  C. G. Torre
; I. M. Anderson
;  Date: 
23 Feb 1993  Journal:  Phys.Rev.Lett. 70 (1993) 35253529  Subject:  grqc  Abstract:  Generalized symmetries of the Einstein equations are infinitesimal transformations of the spacetime metric that formally map solutions of the Einstein equations to other solutions. The infinitesimal generators of these symmetries are assumed to be local, ie at a given spacetime point they are functions of the metric and an arbitrary but finite number of derivatives of the metric at the point. We classify all generalized symmetries of the vacuum Einstein equations in four spacetime dimensions and find that the only generalized symmetry transformations consist of: (i) constant scalings of the metric (ii) the infinitesimal action of generalized spacetime diffeomorphisms. Our results rule out a large class of possible ``observables’’ for the gravitational field, and suggest that the vacuum Einstein equations are not integrable.  Source:  arXiv, grqc/9302033  Other source:  [GID 574806] pmid10053896  Services:  Forum  Review  PDF  Favorites 


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