Gauge-invariant gravitational perturbations of maximally symmetric spacetimes

TL;DR

The paper develops a gauge-invariant formalism for linear gravitational perturbations of maximally symmetric spacetimes, including AdS, with an emphasis on AdS/CFT and brane-world contexts. It constructs gauge-invariant variables and demonstrates the existence of scalar-type master variables that obey master equations, unifying scalar, vector, and tensor perturbations in the case $D-n=2$. The work provides explicit expressions for the Einstein-equation-forms in terms of these variables and derives master equations with detailed conditions on auxiliary constants and source terms, enabling a reduction to scalar master variables $\Phi_{(S)}$, $\Phi_{(V)}$, and $F_{(T)}$. This framework advances the analysis of bulk perturbations, clarifies the nonlocal evolution in brane-world cosmology, and lays groundwork for incorporating Israel junction conditions, with potential applications to Schwarzschild-AdS bulk geometries.

Abstract

Gravitational perturbations of anti-deSitter spacetime play important roles in AdS/CFT correspondence and the brane world scenario. In this paper, we develop a gauge-invariant formalism of gravitational perturbations of maximally symmetric spacetimes including anti-deSitter spacetime. Existence of scalar-type master variables is shown and the corresponding master equations are derived.