Energy and momentum from the Palatini formalism

I derive from the Palatini formalism, in which metric and affinity are varied independently, an energy-momentum complex qualitatively different in form from the usual energy-momentum representations of general relativity. A similar procedure can be carried out for electrodynamics, illuminating by analogy the structure of the gravitational Lagrangian. The new energy density vanishes for all static vacuum solutions of the Einstein equations, and the radiated energy from an isolated system in an asymptotically flat space in general diverges. These facts suggest that the formalism could be used to express Mach's principle.