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

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