Multisymplectic formulation of Lagrangian models in gravitation
Jordi Gaset, Narciso Román-Roy
TL;DR
The work recasts General Relativity in the language of multisymplectic field theory, analyzing two vacuum Lagrangian formulations: the Einstein-Hilbert model with a higher-order singular Lagrangian and the Einstein-Palatini model with a first-order singular Lagrangian. It employs jet-bundle geometry and multivector fields to construct premultisymplectic structures and applies a constraint algorithm to identify final constraint submanifolds where the dynamics unfold. In the EH case, the Einstein equations emerge on a final submanifold as the Euler–Lagrange equations. In the EP case, metricity and torsion constraints generate a richer first-order, gauge-dependent dynamics, which can be partially fixed to recover the EH theory, providing a unified geometric framework for GR formulations.
Abstract
We apply the multisymplectic formulation of classical field theories [11, 12, 14] to describe the Einstein-Hilbert and the Einstein-Palatini (or metric-affine) Lagrangian models of General Relativity.