Variational theory of the Ricci curvature tensor dynamics

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 $$R^{\mu \nu }$$ R μ ν rather than the metric tensor $$g_{\mu \nu }$$ g μ ν . The corresp...

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Autores principales:	Claudio Cremaschini, Jiří Kovář, Zdeněk Stuchlík, Massimo Tessarotto
Formato:	article
Lenguaje:	EN
Publicado:	SpringerOpen 2021
Materias:	Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
Acceso en línea:	https://doaj.org/article/2d3956fc4cde495fb8d44e09369f01d7
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spelling	oai:doaj.org-article:2d3956fc4cde495fb8d44e09369f01d72021-11-28T12:11:36ZVariational theory of the Ricci curvature tensor dynamics10.1140/epjc/s10052-021-09847-61434-60441434-6052https://doaj.org/article/2d3956fc4cde495fb8d44e09369f01d72021-11-01T00:00:00Zhttps://doi.org/10.1140/epjc/s10052-021-09847-6https://doaj.org/toc/1434-6044https://doaj.org/toc/1434-6052Abstract 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 $$R^{\mu \nu }$$ R μ ν rather than the metric tensor $$g_{\mu \nu }$$ g μ ν . The corresponding Lagrangian function, denoted as $$L_{R}$$ L R , is realized by a polynomial expression of the Ricci 4-scalar $$R\equiv g_{\mu \nu }R^{\mu \nu }$$ R ≡ g μ ν R μ ν and of the quadratic curvature 4-scalar $$\rho \equiv R^{\mu \nu }R_{\mu \nu }$$ ρ ≡ R μ ν R μ 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 $$\Lambda >0$$ 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.Claudio CremaschiniJiří KovářZdeněk StuchlíkMassimo TessarottoSpringerOpenarticleAstrophysicsQB460-466Nuclear and particle physics. Atomic energy. RadioactivityQC770-798ENEuropean Physical Journal C: Particles and Fields, Vol 81, Iss 11, Pp 1-7 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798
spellingShingle	Astrophysics QB460-466 Nuclear and particle physics. Atomic energy. Radioactivity QC770-798 Claudio Cremaschini Jiří Kovář Zdeněk Stuchlík Massimo Tessarotto Variational theory of the Ricci curvature tensor dynamics
description	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 $$R^{\mu \nu }$$ R μ ν rather than the metric tensor $$g_{\mu \nu }$$ g μ ν . The corresponding Lagrangian function, denoted as $$L_{R}$$ L R , is realized by a polynomial expression of the Ricci 4-scalar $$R\equiv g_{\mu \nu }R^{\mu \nu }$$ R ≡ g μ ν R μ ν and of the quadratic curvature 4-scalar $$\rho \equiv R^{\mu \nu }R_{\mu \nu }$$ ρ ≡ R μ ν R μ 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 $$\Lambda >0$$ 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.
format	article
author	Claudio Cremaschini Jiří Kovář Zdeněk Stuchlík Massimo Tessarotto
author_facet	Claudio Cremaschini Jiří Kovář Zdeněk Stuchlík Massimo Tessarotto
author_sort	Claudio Cremaschini
title	Variational theory of the Ricci curvature tensor dynamics
title_short	Variational theory of the Ricci curvature tensor dynamics
title_full	Variational theory of the Ricci curvature tensor dynamics
title_fullStr	Variational theory of the Ricci curvature tensor dynamics
title_full_unstemmed	Variational theory of the Ricci curvature tensor dynamics
title_sort	variational theory of the ricci curvature tensor dynamics
publisher	SpringerOpen
publishDate	2021
url	https://doaj.org/article/2d3956fc4cde495fb8d44e09369f01d7
work_keys_str_mv	AT claudiocremaschini variationaltheoryofthericcicurvaturetensordynamics AT jirikovar variationaltheoryofthericcicurvaturetensordynamics AT zdenekstuchlik variationaltheoryofthericcicurvaturetensordynamics AT massimotessarotto variationaltheoryofthericcicurvaturetensordynamics
_version_	1718408128697991168

Variational theory of the Ricci curvature tensor dynamics

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