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Phys. Rev. D 70, 064002 (2004) [6 pages]

Nonlinear N-parameter spacetime perturbations: Gauge transformations

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Carlos F. Sopuerta1,2, Marco Bruni1, and Leonardo Gualtieri3
1Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 2EG, United Kingdom
2Institute for Gravitational Physics and Geometry and Center for Gravitational Wave Physics, Penn State University, University Park, Pennsylvania 16802, USA
3Dipartimento di Fisica “G. Marconi”, Università di Roma “La Sapienza” and Sezione INFN ROMA 1, piazzale Aldo Moro 2, I–00185 Roma, Italy

Received 31 October 2003; published 2 September 2004

We introduce N-parameter perturbation theory as a new tool for the study of nonlinear relativistic phenomena. The main ingredient in this formulation is the use of the Baker-Campbell-Hausdorff formula. The associated machinery allows us to prove the main results concerning the consistency of the scheme to any perturbative order. Gauge transformations and conditions for gauge invariance at any required order can then be derived from a generating exponential formula via a simple Taylor expansion. We outline the relation between our novel formulation and previous developments.

© 2004 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.70.064002
DOI:
10.1103/PhysRevD.70.064002
PACS:
04.25.Nx, 02.40.–k, 95.30.Sf
 
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