Universality of Einstein Equations for the Ricci Squared Lagrangians

Abstract

It has been recently shown that, in the first order (Palatini) formalism, there is universality of Einstein equations and Komar energy-momentum complex, in the sense that for a generic nonlinear Lagrangian depending only on the scalar curvature of a metric and a torsionless connection one always gets Einstein equations and Komar's expression for the energy-momentum complex. In this paper a similar analysis (also in the framework of the first order formalism) is performed for all nonlinear Lagrangians depending on the (symmetrized) Ricci square invariant. The main result is that the universality of Einstein equations and Komar energy-momentum complex also extends to this case (modulo a conformal transformation of the metric).