TY - JOUR

T1 - Perturbations of spacetime

T2 - gauge transformations and gauge invariance at second order and beyond

AU - Bruni, Marco

AU - Matarrese, Sabino

AU - Mollerach, Silvia

AU - Sonego, Sebastiano

PY - 1997/9/1

Y1 - 1997/9/1

N2 - We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second-and higher-order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Secondly, we define gauge invariance to an arbitrary order n. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well as in other spacetime theories. As a specific example, we consider here second-order perturbations in cosmology, assuming a 7 flat Robertson-Walker background, giving explicit second-order transformations between the synchronous and the Poisson (generalized longitudinal) gauges.

AB - We consider in detail the problem of gauge dependence that exists in relativistic perturbation theory, going beyond the linear approximation and treating second-and higher-order perturbations. We first derive some mathematical results concerning the Taylor expansion of tensor fields under the action of one-parameter families (not necessarily groups) of diffeomorphisms. Secondly, we define gauge invariance to an arbitrary order n. Finally, we give a generating formula for the gauge transformation to an arbitrary order and explicit rules to second and third order. This formalism can be used in any field of applied general relativity, such as cosmological and black hole perturbations, as well as in other spacetime theories. As a specific example, we consider here second-order perturbations in cosmology, assuming a 7 flat Robertson-Walker background, giving explicit second-order transformations between the synchronous and the Poisson (generalized longitudinal) gauges.

UR - http://www.scopus.com/inward/record.url?scp=0031507536&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/14/9/014

DO - 10.1088/0264-9381/14/9/014

M3 - Article

AN - SCOPUS:0031507536

SN - 0264-9381

VL - 14

SP - 2585

EP - 2606

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 9

ER -