First-order Lagrangian and Hamiltonian of Lovelock gravity

Pablo Guilleminot, Félix Louis Julié, Nelson Merino, Rodrigo Olea

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number105004
JournalClassical and Quantum Gravity
Issue number10
Publication statusPublished - May 2021


  • Classical mechanics
  • General relativity
  • Modified theories of gravity

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)


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