The second-order problem for k-presymplectic Lagrangian field theories: application to the Einstein–Palatini model

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Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2022-01

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en

Pages

25

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, Volume 116, issue 1

Abstract

In general, the system of 2nd-order partial differential equations made of the Euler–Lagrange equations of classical field theories are not compatible for singular Lagrangians. This is the so-called second-order problem. The first aim of this work is to develop a fully geometric constraint algorithm which allows us to find a submanifold where the Euler–Lagrange equations have solution, and split the constraints into two kinds depending on their origin. We do so using k-symplectic geometry, which is the simplest intrinsic description of classical field theories. As a second aim, the Einstein–Palatini model of General Relativity is studied using this algorithm.

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Funding Information: We acknowledge the financial support from the Spanish Ministerio de Ciencia, Innovación y Universidades project PGC2018-098265-B-C33 and the Secretary of University and Research of the Ministry of Business and Knowledge of the Catalan Government project 2017-SGR-932. Publisher Copyright: © 2021, The Author(s).

Keywords

Classical field theories, Einstein–Palatini model, k-symplectic manifolds, Lagrangian formalism

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Citation

Adame-Carrillo, D, Gaset, J & Román-Roy, N 2022, ' The second-order problem for k-presymplectic Lagrangian field theories : application to the Einstein–Palatini model ', Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, vol. 116, no. 1, 20 . https://doi.org/10.1007/s13398-021-01136-x