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@article{57444, author = {Cremaschini, Claudio and Kovář, Jiří and Stuchlík, Zdeněk and Tessarotto, Massimo}, article_location = {New York (USA)}, article_number = {11}, doi = {http://dx.doi.org/10.1140/epjc/s10052-021-09847-6}, keywords = {field}, language = {eng}, issn = {1434-6044}, journal = {European Physical Journal C}, title = {Variational theory of the Ricci curvature tensor dynamics}, url = {https://epjc.epj.org/articles/epjc/abs/2021/11/10052_2021_Article_9847/10052_2021_Article_9847.html}, volume = {81}, year = {2021} }
TY - JOUR ID - 57444 AU - Cremaschini, Claudio - Kovář, Jiří - Stuchlík, Zdeněk - Tessarotto, Massimo PY - 2021 TI - Variational theory of the Ricci curvature tensor dynamics JF - European Physical Journal C VL - 81 IS - 11 SP - "1030-1"-"1030-7" EP - "1030-1"-"1030-7" PB - SPRINGER SN - 14346044 KW - field UR - https://epjc.epj.org/articles/epjc/abs/2021/11/10052_2021_Article_9847/10052_2021_Article_9847.html N2 - 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. rather than the metric tensor g mu.. The corresponding Lagrangian function, denoted as L R, is realized by a polynomial expression of the Ricci 4-scalar R = g mu. R mu. and of the quadratic curvature 4scalar. = R mu. R mu.. 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 similar to > 0. Then, by implementing the deDonder-Weyl formalism, the physical conditions for the existence of amanifestly-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. ER -
CREMASCHINI, Claudio, Jiří KOVÁŘ, Zdeněk STUCHLÍK a Massimo TESSAROTTO. Variational theory of the Ricci curvature tensor dynamics. \textit{European Physical Journal C}. New York (USA): SPRINGER, 2021, roč.~81, č.~11, s.~''1030-1''-''1030-7'', 7 s. ISSN~1434-6044. Dostupné z: https://dx.doi.org/10.1140/epjc/s10052-021-09847-6.
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