Fourth derivative gravity in the auxiliary fields representation and application to the black hole stability

TL;DR

This paper reformulates fourth-order gravity using auxiliary fields, simplifying perturbation analysis, and applies it to study Schwarzschild black hole stability, clarifying the role of unphysical ghosts.

Contribution

It introduces an auxiliary fields formulation for fourth-order gravity, making perturbation analysis more transparent and providing new insights into black hole stability.

Findings

Auxiliary fields simplify perturbation calculations.

Equivalence with standard metric formulation established.

Insights into the role of unphysical ghosts in the theory.

Abstract

We consider an auxiliary fields formulation for the general fourth-order gravity on an arbitrary curved background. The case of a Ricci-flat background is elaborated in full details and it is shown that there is an equivalence with the standard metric formulation. At the same time, using auxiliary fields helps to make perturbations to look simpler and the results more clear. As an application we reconsider the linear perturbations for the classical Schwarzschild solution. We also briefly discuss the relation to the effect of massive unphysical ghosts in the theory.