First-order Lagrangian and Hamiltonian of Lovelock gravity

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Abstract
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 π ij δh ij , where π ij is the canonical momentum conjugate to the boundary metric h ij . Then, the first-order Lagrangian density is obtained either by integration of π ij over the metric derivative ∂ w h ij normal to the boundary, or by rewriting the Myers term as a bulk term.
Funding Information
  • NSF (AST-2006538 PHY-1912550)
  • NASA ATP (17-ATP17-0225 19-ATP19-0051)
  • NSF-XSEDE (PHY- 090003)
  • H2020 Marie Skłodowska-Curie Actions (690904)
  • Fondo Nacional de Desarrollo Científico y Tecnológico (11180894 1170765)
  • GWverse COST Action (CA16104)

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