Energy-momentum complex for nonlinear gravitational Lagrangians in the first-order formalism

It has been recently shown that there is universality of Einstein equations, in the first-order (Palatini) formalism, 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. In this paper the energy-density flow for nonlinear gravitational Lagrangians is investigated in this formalism. It is shown that in the generic case the energy-momentum complex does not depend on the Lagrangian and is in fact equal to the Komar complex, known in the purely metric formalism for the standard linear Hilbert Lagrangian.On leave from the Institute of Theoretical Physics, University of Wrocaw, pl. Maxa Borna 9, 50-204 Wrocaw, Poland