Symmetries of the Einstein Equations

Details Symmetries of the Einstein Equations Symmetries of the Einstein Equations

1993-02-23

arxiv.org/abs/gr-qc/9302033v1

Phys.Rev.Lett. 70 (1993) 3525-3529

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

15 pages, FTG-114-USU, Plain TeX

Scientific paper

10.1103/PhysRevLett.70.3525

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.

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