TESSAROTTO, Massimo and Claudio CREMASCHINI. The Principle of Covariance and the Hamiltonian Formulation of General Relativity. Entropy. 2021, vol. 23, No 2, p. "215-1"-"215-33", 33 pp. ISSN 1099-4300. Available from: https://dx.doi.org/10.3390/e23020215.
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Basic information
Original name The Principle of Covariance and the Hamiltonian Formulation of General Relativity
Authors TESSAROTTO, Massimo (380 Italy, belonging to the institution) and Claudio CREMASCHINI (380 Italy, belonging to the institution).
Edition Entropy, 2021, 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/47813059:19630/21:A0000168
Organization unit Institute of physics in Opava
Doi http://dx.doi.org/10.3390/e23020215
UT WoS 000622501300001
Keywords in English Einstein-Hilbert variational principle;Hamiltonian theory of GR;ADM Hamiltonian theory;manifest covariance
Tags 2022, FÚ, RIV22
Tags International impact, Reviewed
Changed by Changed by: Mgr. Pavlína Jalůvková, učo 25213. Changed: 11/3/2022 09:58.
Abstract
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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