Publication date: Nov 2021
Abstract:
In this letter a new Lagrangian variational principle is proved to hold for the Einstein field equations, in which the independent variational tensor field is identified with the Ricci curvature tensor Rμ ν rather than the metric tensor gμ ν. The corresponding Lagrangian function, denoted as LR, is realized by a polynomial expression of the Ricci 4-scalar R ≡gμ νRμ ν and of the quadratic curvature 4-scalar ρ ≡Rμ νRμ ν . The Lagrangian variational principle applies both to vacuum and non-vacuum cases and for its validity it demands a non-vanishing, and actually also positive, cosmological constant Λ >0 . Then, by implementing the deDonder-Weyl formalism, the physical conditions for the existence of a manifestly-covariant Hamiltonian structure associated with such a Lagrangian formulation are investigated. As a consequence, it is proved that the Ricci tensor can obey a Hamiltonian dynamics which is consistent with the solutions predicted by the Einstein field equations.
Authors:
Cremaschini, Claudio; Kovář, Jiří; Stuchlík, Zdeněk; Tessarotto, Massimo;