Recursive structure in the definitions of gauge-invariant variables for any order perturbations

Abstract

The construction of gauge-invariant variables for any order perturbations is discussed. Explicit constructions of the gauge-invariant variables for perturbations to 4th order are shown. From these explicit construction, the recursive structure in the definitions of gauge-invariant variables for any order perturbations is found. Through this recursive structure, the correspondence with the fully non-linear exact perturbations is briefly discussed.

21 pages, no figure: (v2) one section and additional explanations are added. Accepted for publication to Classical and Quantum Gravity

References in corpus (3)

• Gauge-invariant Formulation of the Second-order Cosmological Perturbations
• Consistency of Equations in the Second-order Gauge-invariant Cosmological Perturbation Theory
• Gauge-invariant variables in general-relativistic perturbations: globalization and zero-mode problem

Cited by in corpus (1)

• Comparing a gauge-invariant formulation and a "conventional complete gauge-fixing approach" for $l=0,1$ mode perturbations on the Schwarzschild background spacetime