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 the Myers boundary term, which guarantees a Dirichlet variational principle with a surface term of the form πi jδhi j, where πi j is the canonical momentum conjugate to the boundary metric hi j. Then, the first-order Lagrangian density is obtained either by integration of πi j over the metric derivative ∂whi j normal to the boundary, or by rewriting the Myers term as a bulk term.
- Classical mechanics
- General relativity
- Modified theories of gravity
ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)