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The Principle of Covariance and the Hamiltonian Formulation of General Relativity

The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory. Preliminarily, customary Lagrangian variational pr...

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Autores principales: Tessarotto, Massimo, Cremaschini, Claudio
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7916769/
https://www.ncbi.nlm.nih.gov/pubmed/33579013
http://dx.doi.org/10.3390/e23020215
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author Tessarotto, Massimo
Cremaschini, Claudio
author_facet Tessarotto, Massimo
Cremaschini, Claudio
author_sort Tessarotto, Massimo
collection PubMed
description The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory. Preliminarily, customary Lagrangian variational principles are reviewed, pointing out the existence of a novel variational formulation in which the class of variations remains unconstrained. As a second step, the conditions of validity of the non-manifestly covariant ADM variational theory are questioned. The main result concerns the proof of its intrinsic non-Hamiltonian character and the failure of this approach in providing a symplectic structure of space-time. In contrast, it is demonstrated that a solution reconciling the physical requirements of covariance and manifest covariance of variational theory with the existence of a classical Hamiltonian structure for the gravitational field can be reached in the framework of synchronous variational principles. Both path-integral and volume-integral realizations of the Hamilton variational principle are explicitly determined and the corresponding physical interpretations are pointed out.
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spelling pubmed-79167692021-03-01 The Principle of Covariance and the Hamiltonian Formulation of General Relativity Tessarotto, Massimo Cremaschini, Claudio Entropy (Basel) Article The implications of the general covariance principle for the establishment of a Hamiltonian variational formulation of classical General Relativity are addressed. The analysis is performed in the framework of the Einstein-Hilbert variational theory. Preliminarily, customary Lagrangian variational principles are reviewed, pointing out the existence of a novel variational formulation in which the class of variations remains unconstrained. As a second step, the conditions of validity of the non-manifestly covariant ADM variational theory are questioned. The main result concerns the proof of its intrinsic non-Hamiltonian character and the failure of this approach in providing a symplectic structure of space-time. In contrast, it is demonstrated that a solution reconciling the physical requirements of covariance and manifest covariance of variational theory with the existence of a classical Hamiltonian structure for the gravitational field can be reached in the framework of synchronous variational principles. Both path-integral and volume-integral realizations of the Hamilton variational principle are explicitly determined and the corresponding physical interpretations are pointed out. MDPI 2021-02-10 /pmc/articles/PMC7916769/ /pubmed/33579013 http://dx.doi.org/10.3390/e23020215 Text en © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Tessarotto, Massimo
Cremaschini, Claudio
The Principle of Covariance and the Hamiltonian Formulation of General Relativity
title The Principle of Covariance and the Hamiltonian Formulation of General Relativity
title_full The Principle of Covariance and the Hamiltonian Formulation of General Relativity
title_fullStr The Principle of Covariance and the Hamiltonian Formulation of General Relativity
title_full_unstemmed The Principle of Covariance and the Hamiltonian Formulation of General Relativity
title_short The Principle of Covariance and the Hamiltonian Formulation of General Relativity
title_sort principle of covariance and the hamiltonian formulation of general relativity
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7916769/
https://www.ncbi.nlm.nih.gov/pubmed/33579013
http://dx.doi.org/10.3390/e23020215
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