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Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond
Open accessAbstract
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.
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Cites
Gauge-invariant cosmological perturbations
Bardeen, J. M. (1980) · Physical Review D · doi:10.1103/physrevd.22.1882 · Cited by 2,393
Does back reaction enforce the averaged null energy condition in semiclassical gravity?
Flanagan, E. E., & Wald, R. M. (1996) · Physical Review D · doi:10.1103/physrevd.54.6233 · Cited by 352
Cited by
Quasi-Normal Modes of Stars and Black Holes
Kokkotas, K. D., & Schmidt, B. G. (1999) · Living Reviews in Relativity · doi:10.12942/lrr-1999-2 · Cited by 2,055
A general proof of the conservation of the curvature perturbation
Lyth, D. H., Malik, K. A., & Sasaki, M. (2005) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2005/05/004 · Cited by 804
Teleparallel gravity: from theory to cosmology
Bahamonde, S., Dialektopoulos, K. F., Escamilla-Rivera, C., Farrugia, G., Gakis, V., Hendry, M., Hohmann, M., Levi Said, J., Mifsud, J., & Di Valentino, E. (2023) · Reports on Progress in Physics · doi:10.1088/1361-6633/ac9cef · Cited by 503
Energy-momentum tensor for cosmological perturbations
Abramo, L. R. W., Brandenberger, R. H., & Mukhanov, V. F. (1997) · Physical Review D · doi:10.1103/physrevd.56.3248 · Cited by 295
CMB polarization from secondary vector and tensor modes
Mollerach, S., Harari, D., & Matarrese, S. (2004) · Physical Review D · doi:10.1103/physrevd.69.063002 · Cited by 289
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Metadata
- Authors
- Bruni, M., Matarrese, S., Mollerach, S., & Sonego, S.
- Venue
- Classical and Quantum Gravity
- Publisher
- IOP Publishing
- Published
- 1997-09-01
- Volume
- 14
- Issue
- 9
- Pages
- 2585-2606
- ISSN
- 0264-9381 (ISSN-L)
- 1361-6382
- OpenAlex
- W2061835457
- Cited by
- 343
- References
- 2
- FWCI
- 5.92
- Type
- journal article
- Language
- en
- Open access
- bronze
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- Bruni, M., Matarrese, S., Mollerach, S., & Sonego, S. (1997). Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond. Classical and Quantum Gravity. https://doi.org/10.1088/0264-9381/14/9/014
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