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.

中文翻译：

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洛夫洛克引力的格里菲斯变分多辛公式

这项工作主要致力于构建洛夫洛克引力的多辛描述，这是广义相对论的延伸。我们为洛夫洛克拉格朗日量建立格里菲斯变分问题，得到相应场方程的几何形式。我们给出了该模型的统一拉格朗日-哈密尔顿公式，并研究了爱因斯坦-希尔伯特和爱因斯坦-帕拉蒂尼引力模型的统一公式之间的对应关系。