Palatini variation of curvature-squared action and gravitational collapse

It is shown that Palatini variation of a class of gravitational actions based on a quadratic generalization of the Einstein-Hilbert action results in a metric-incompatible theory of gravity but one that satisfies Birkhoff's theorem. The usual fourth-order field equations are replaced by two second-order equations. Application of the field equations to a model of freely falling dust are discussed.