On the Hamiltonian of Gravity Theories Whose Action is Linear in Spacetime Curvature

Abstract

A straightforward method to compute Hamilton's density for theories that are linear in the spacetime curvature is provided. It is shown that the lapse function and shift vector still give rise to primary constraints, while the induced metric gives rise to nontrivial evolution equations. The corresponding Hamilton's density can always be obtained, albeit in a formal sense.