Griffiths variational multisymplectic formulation for Lovelock gravity

Abstract

This work is mainly devoted to constructing a multisymplectic description of Lovelock's gravity, which is an extension of General Relativity. We establish the 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.

Symmetries and gauge symmetries in multisymplectic first and second-order Lagrangian field theories: electromagnetic and gravitational fields

“…Following this guidelines, all this methods could be applied to investigate Noether symmetries and conservation laws, as well as gauge symmetries for other theories of gravity (for instance, Chern-Simons gravity) and other extended models of General Relativity [3,6,8,16].…”

“…As G ⊂ ker Ω L , for every Z ∈ G we have that i(Z)ΩL = 0, then L(Z)ΩL = 0. Therefore every gauge vector field is an infinitesimal Cartan symmetry and then a symmetry (Proposition 1), and hence, if it is also a holonomic vector field, it transforms holonomic solutions to the field equations into holonomic solutions (see (6)). Incidentally, any closed m − 1-forms can be thought as an associated local Hamiltonian form to any gauge vector field.…”

Routh Reduction of Palatini Gravity in Vacuum

“…is flat, a restriction far more stringent than those imposed by the metricity conditions, that only require the associated connection form to have values in k. For a description of these admissible variations in the case of the metricity constraints, see [7,Section 4.1].…”

“…instead, they must be thought as infinitesimal symmetries of the metricity conditions. We will not explore further this topic here; the interested reader can find a detailed study of these questions in [7]. On the other hand, the usual variational problem for Einstein-Hilbert gravity is given by the triple…”

Multisymplectic formalism for cubic horndeski theories

“…Other relevant examples of applications of the multisymplectic formalism are the metric-affine gravity with [42,43] and without vielbein [44], Lovelock Gravity [45] and Chern-Simons gravity and the bosonic string [46]. There is also a proposal for a covariant renormalizable field theory of gravity [47].…”