TY - JOUR

T1 - Gauge dependence in the theory of non-linear spacetime perturbations

AU - Sonego, Sebastiano

AU - Bruni, Marco

PY - 1998/4/1

Y1 - 1998/4/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0032381598&partnerID=8YFLogxK

U2 - 10.1007/s002200050325

DO - 10.1007/s002200050325

M3 - Article

AN - SCOPUS:0032381598

SN - 0010-3616

VL - 193

SP - 209

EP - 218

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 1

ER -