DPSV trick for spherically symmetric backgrounds

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 L3 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 L4 Horndeski theory.