Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2001-12-16
Phys.Rev. D65 (2002) 084048
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
RevTex, 5 pages, sign errors corrected. Section 2 enlarged
Scientific paper
10.1103/PhysRevD.65.084048
We deal with the problem of identifying a background structure and its perturbation in tetrad theories of gravity. Starting from a peculiar trivial principal bundle we define a metric which depends only on the gauge connection. We find the allowed four-dimensional structure groups; two of them turn out to be the translation group T_4 and the unitary group U(2). When the curvature vanishes the metric reduces to its background form which coincides with Minkowski flat metric for the T_4 case and with the Einstein static universe metric for the U(2) case. The perturbation has a coordinate independent definition and allows for the introduction of observables distinguished from those obtained from the metric alone. Finally, we show that any teleparallel theory of gravity, and hence general relativity, can be considered as a gauge theory over the groups introduced.
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