First-order Lagrangian and Hamiltonian of Lovelock gravity

Based on the insight gained by many authors over the years on the structure of the 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 and associated Hamiltonian. To do so, we start from the Lovelock Lagrangian supplemented with theMyers boundary term, which guarantees a Dirichlet variational principle with a surface term of the form pi jdhi j, where pi j is the canonical momentum conjugate to the boundary metric hi j. Then, the first-order Lagrangian density is obtained either by integration of pi j over the metric derivative.whi j normal to the boundary, or by rewriting the Myers term as a bulk term.