The Principle of Covariance and the Hamiltonian Formulation of General Relativity

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19630%2F21%3AA0000168" target="_blank" >RIV/47813059:19630/21:A0000168 - isvavai.cz</a>

Result on the web

<a href="https://www.mdpi.com/1099-4300/23/2/215" target="_blank" >https://www.mdpi.com/1099-4300/23/2/215</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/e23020215" target="_blank" >10.3390/e23020215</a>

Result language

angličtina

Original language name

The Principle of Covariance and the Hamiltonian Formulation of General Relativity

Original language 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.

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

2021

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

23

Issue of the periodical within the volume

2

Country of publishing house

CH - SWITZERLAND

Number of pages

33

Pages from-to

„215-1“-„215-33“

UT code for WoS article

000622501300001

EID of the result in the Scopus database

2-s2.0-85100944477