Griffiths Variational Multisymplectic Formulation for Lovelock Gravity

TL;DR

This paper develops a multisymplectic geometric framework for Lovelock gravity, extending the variational and Hamiltonian formalisms of General Relativity to higher-order curvature theories.

Contribution

It introduces a Griffiths variational approach and a unified Lagrangian-Hamiltonian formulation for Lovelock gravity, linking it to Einstein models.

Findings

Established a multisymplectic structure for Lovelock gravity

Derived the geometric form of Lovelock field equations

Connected Lovelock and Einstein gravity formulations

Abstract

This work is mainly devoted to constructing a multisymplectic description of Lovelock's gravity, which is an extension of General Relativity. We establish a Griffiths variational problem for the Lovelock Lagrangian, obtaining the geometric form of the corresponding field equations. We give the unified Lagrangian--Hamiltonian formulation of this model and we study the correspondence between the unified formulations for the Einstein--Hilbert and the Einstein--Palatini models of gravity.