Non-Linear N-Parameter Spacetime Perturbations: Gauge Transformations

Abstract

We introduce N-parameter perturbation theory as a new tool for the study of non-linear 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.

7 pages, no figures, RevTeX 4.0. Revised version to match version published in PRD

References in corpus (9)

• Second-Order Cosmological Perturbations from Inflation
• CMB polarization from secondary vector and tensor modes
• Dark energy from backreaction
• The Separate Universe Approach and the Evolution of Nonlinear Superhorizon Cosmological Perturbations
• Non-radial oscillation modes as a probe of density discontinuities in neutron stars
• Gauge Invariant Variables in Two-Parameter Nonlinear Perturbations
• Two-parameter non-linear spacetime perturbations: gauge transformations and gauge invariance
• On second-order superhorizon perturbations in multifield inflationary models
• Comparison of the oscillatory behaviors of a gravitating Nambu-Goto string with a test string

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