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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 and Massimo TESSAROTTO. Variational theory of the Ricci curvature tensor dynamics. \textit{European Physical Journal C}. New York (USA): SPRINGER, 2021, vol.~81, No~11, p.~''1030-1''-''1030-7'', 7 pp. ISSN~1434-6044. Available from: https://dx.doi.org/10.1140/epjc/s10052-021-09847-6.
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