DPSV trick for spherically symmetric backgrounds

TL;DR

This paper evaluates the DPSV approach for analyzing linear perturbations in Horndeski theories around spherically symmetric backgrounds, confirming its validity in a specific subclass but identifying its limitations in more general cases.

Contribution

It proves the validity of the DPSV approach in the $ olinebreak ext{L}_3$ subclass of Horndeski theories and shows its failure in the more general $ olinebreak ext{L}_4$ case.

Findings

DPSV approach is valid in $ ext{L}_3$ Horndeski theories for static, spherically symmetric backgrounds.

The DPSV trick corresponds to a specific gauge choice in the quadratic action.

The DPSV approach does not work in the more general $ ext{L}_4$ Horndeski theories.

Abstract

We discuss the approach suggested by Deffayet et al. (DPSV) to analysing the linearized perturbations in Horndeski theory in the case of a static, spherically symmetric background. In $\mathcal{L}_3$ subclass of Horndeski theories we prove the validity of the DPSV approach by showing that the original method corresponds to a specific gauge choice in the quadratic action for perturbations. We also show that in the case of a spherically symmetric background the DPSV trick does not work in a more general $\mathcal{L}_4$ Horndeski theory.