First-order Lagrangian and Hamiltonian of Lovelock gravity

Abstract Based on the insight gained by many authors over years structure of Einstein–Hilbert, Gauss–Bonnet and Lovelock gravity Lagrangians, we show how to derive-in an elementary fashion-their first-order, generalized ‘Arnowitt–Deser–Misner’ Lagrangian associated Hamiltonian. To do so, start from supplemented with Myers boundary term, which guarantees a Dirichlet variational principle surface term form ? ij ?h , where is canonical momentum conjugate metric h . Then, first-order density obtained either integration derivative ? w normal boundary, or rewriting as bulk term.