Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-08-28
Commun.Math.Phys. 193 (1998) 209-218
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
paper accepted for publication in Communications of Mathematical Physics; SISSA preprint 105/97/A. 10 pages and 2 figures, sta
Scientific paper
10.1007/s002200050325
Diffeomorphism freedom induces a gauge dependence in the theory of spacetime perturbations. We derive a compact formula for gauge transformations of perturbations of arbitrary order. To this end, we develop the theory of Taylor expansions for one-parameter families (not necessarily groups) of diffeomorphisms. First, we introduce the notion of knight diffeomorphism, that generalises the usual concept of flow, and prove a Taylor's formula for the action of a knight on a general tensor field. Then, we show that any one-parameter family of diffeomorphisms can be approximated by a family of suitable knights. Since in perturbation theory the gauge freedom is given by a one-parameter family of diffeomorphisms, the expansion of knights is used to derive our transformation formula. The problem of gauge dependence is a purely kinematical one, therefore our treatment is valid not only in general relativity, but in any spacetime theory.
Bruni Marco
Sonego Sebastiano
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