First-order equivalent to Einstein-Hilbert Lagrangian

Abstract

A first-order Lagrangian $L^{\nabla }$ variationally equivalent to the second-order Einstein-Hilbert Lagrangian is introduced. Such a Lagrangian depends on a symmetric linear connection, but the dependence is covariant under diffeomorphisms. The variational problem defined by $L^{\nabla }$ is proved to be regular and its Hamiltonian formulation is studied, including its covariant Hamiltonian attached to $\nabla$.

References in corpus (1)

• On the equivalence of the Einstein-Hilbert and the Einstein-Palatini formulations of general relativity for an arbitrary connection