CREMASCHINI, Claudio and Massimo TESSAROTTO. Unconstrained Lagrangian Variational Principles for the Einstein Field Equations. Entropy. 2023, vol. 25, No 2, p. "337-1"-"337-27", 27 pp. ISSN 1099-4300. Available from: https://dx.doi.org/10.3390/e25020337.
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Basic information
Original name Unconstrained Lagrangian Variational Principles for the Einstein Field Equations
Authors CREMASCHINI, Claudio (380 Italy, belonging to the institution) and Massimo TESSAROTTO (380 Italy, belonging to the institution).
Edition Entropy, 2023, 1099-4300.
Other information
Original language English
Type of outcome Article in a journal
Field of Study 10308 Astronomy
Country of publisher Switzerland
Confidentiality degree is not subject to a state or trade secret
WWW URL
RIV identification code RIV/47813059:19630/23:A0000297
Organization unit Institute of physics in Opava
Doi http://dx.doi.org/10.3390/e25020337
UT WoS 000945040800001
Keywords in English Einstein field equations; Lagrangian variational principles; principle of manifest covariance; unconstrained variational principles
Tags RIV24, UF
Tags International impact, Reviewed
Changed by Changed by: Mgr. Pavlína Jalůvková, učo 25213. Changed: 19/1/2024 10:39.
Abstract
This paper deals with the problem of establishing a systematic theoretical formulation of variational principles for the continuum gravitational field dynamics of classical General Relativity (GR). In this reference, the existence of multiple Lagrangian functions underlying the Einstein field equations (EFE) but having different physical connotations is pointed out. Given validity of the Principle of Manifest Covariance (PMC), a set of corresponding variational principles can be constructed. These are classified in two categories, respectively, referred to as constrained and unconstrained Lagrangian principles. They differ for the normalization properties required to be satisfied by the variational fields with respect to the analogous conditions holding for the extremal fields. However, it is proved that only the unconstrained framework correctly reproduces EFE as extremal equations. Remarkably, the synchronous variational principle recently discovered belongs to this category. Instead, the constrained class can reproduce the Hilbert-Einstein formulation, although its validity demands unavoidably violation of PMC. In view of the mathematical structure of GR based on tensor representation and its conceptual meaning, it is therefore concluded that the unconstrained variational setting should be regarded as the natural and more fundamental framework for the establishment of the variational theory of EFE and the consequent formulation of consistent Hamiltonian and quantum gravity theories.
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