Neighbours of Einstein's Equations: Connections and Curvatures

Details Neighbours of Einstein's Equations: Connections and Curvatures Neighbours of Einstein's Equations: Connections and Curvatures

1995-06-05

arxiv.org/abs/gr-qc/9506007v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, LaTeX

Scientific paper

10.1007/BF02106972

Once the action for Einstein's equations is rewritten as a functional of an SO(3,C) connection and a conformal factor of the metric, it admits a family of ``neighbours'' having the same number of degrees of freedom and a precisely defined metric tensor. This paper analyzes the relation between the Riemann tensor of that metric and the curvature tensor of the SO(3) connection. The relation is in general very complicated. The Einstein case is distinguished by the fact that two natural SO(3) metrics on the GL(3) fibers coincide. In the general case the theory is bimetric on the fibers.

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