Marco Bruni et al 1997 Class. Quantum Grav. 14 2585 doi:10.1088/0264-9381/14/9/014
Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
Marco Bruni
,
, Sabino Matarrese§, Silvia Mollerach and Sebastiano Sonego
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 flat Robertson - Walker background, giving explicit second-order transformations between the synchronous and the Poisson (generalized longitudinal) gauges.
- PACS
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04.25.Nx Post-Newtonian approximation; perturbation theory; related approximations
02.30.Mv Approximations and expansions
04.70.-s Physics of black holes
04.20.Gz Spacetime topology, causal structure, spinor structure
- MSC
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83C05 Einstein's equations (general structure, canonical formalism, Cauchy problems)
41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
- Subjects
- Dates
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Issue 9 (September 1997)
Received 31 December 1996, in final form 20 May 1997
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Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
Marco Bruni et al 1997 Class. Quantum Grav. 14 2585
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