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

David Adame-Carrillo, Jordi Gaset, Narciso Román-Roy*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Article number20
Number of pages25
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Volume116
Issue number1
DOIs
Publication statusPublished - Jan 2022
MoE publication typeA1 Journal article-refereed

Keywords

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

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