Gauge invariant description of weak gravitational field on a spherically symmetric background with cosmological constant

TL;DR

This paper develops a gauge-invariant formalism for analyzing linear gravitational perturbations on a spherically symmetric Kottler background with a cosmological constant, simplifying the extraction of physical information.

Contribution

It introduces a set of four gauge-invariant scalar functions that encode all physical data and reformulates the symplectic form and equations of motion in terms of these invariants.

Findings

Gauge-invariant scalar functions fully describe initial data.

Reformulation of symplectic form and equations of motion.

Exploration of simple solutions within the formalism.

Abstract

We present a formalism for analysis of linear Cauchy data on a Kottler metric. Our method removes redundancy due to gauge transformations and constraints. A set of four gauge-invariant, scalar functions on the Cauchy surface is produced and shown to contain full physical information from the initial data. The symplectic form of the theory and equations of motion are reformulated in terms of these invariants and some simple solutions are explored.