Unconstrained Lagrangian Variational Principles for the Einstein Field Equations

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19630%2F23%3AA0000297" target="_blank" >RIV/47813059:19630/23:A0000297 - isvavai.cz</a>

Result on the web

<a href="https://www.mdpi.com/1099-4300/25/2/337" target="_blank" >https://www.mdpi.com/1099-4300/25/2/337</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/e25020337" target="_blank" >10.3390/e25020337</a>

Result language

angličtina

Original language name

Unconstrained Lagrangian Variational Principles for the Einstein Field Equations

Original language description

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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10308 - Astronomy (including astrophysics,space science)

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Entropy

ISSN

1099-4300

e-ISSN

—

Volume of the periodical

25

Issue of the periodical within the volume

2

Country of publishing house

CH - SWITZERLAND

Number of pages

27

Pages from-to

„337-1“-„337-27“

UT code for WoS article

000945040800001

EID of the result in the Scopus database

2-s2.0-85148936692