Symmetries of the Einstein equations

DOI10.1103/PHYSREVLETT.70.3525zbMATH Open1051.83504arXivgr-qc/9302033OpenAlexW2144916298WikidataQ52394950 ScholiaQ52394950MaRDI QIDQ4492149

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Publication date: 16 July 2000

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/gr-qc/9302033

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