Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond

Marco Bruni*, Sabino Matarrese, Silvia Mollerach, Sebastiano Sonego

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)2585-2606
Number of pages22
JournalClassical and Quantum Gravity
Volume14
Issue number9
DOIs
Publication statusPublished - 1 Sep 1997

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