Energy-momentum tensors in linearized Einstein's theory and massive gravity: The question of uniqueness

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10335387" target="_blank" >RIV/00216208:11320/16:10335387 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1103/PhysRevD.93.024009" target="_blank" >http://dx.doi.org/10.1103/PhysRevD.93.024009</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevD.93.024009" target="_blank" >10.1103/PhysRevD.93.024009</a>

Result language

angličtina

Original language name

Energy-momentum tensors in linearized Einstein's theory and massive gravity: The question of uniqueness

Original language description

The question of the uniqueness of energy-momentum tensors in the linearized general relativity and in the linear massive gravity is analyzed without using variational techniques. We start from a natural ansatz for the form of the tensor (for example, that it is a linear combination of the terms quadratic in the first derivatives), and require it to be conserved as a consequence of field equations. In the case of the linear gravity in a general gauge we find a four-parametric system of conserved second-rank tensors which contains a unique symmetric tensor. This turns out to be the linearized Landau-Lifshitz pseudotensor employed often in full general relativity. We elucidate the relation of the four-parametric system to the expression proposed recently by Butcher et al. "on physical grounds" in harmonic gauge, and we show that the results coincide in the case of high-frequency waves in vacuum after a suitable averaging. In the massive gravity we show how one can arrive at the expression which coincides with the "generalized linear symmetric Landau-Lifshitz" tensor. However, there exists another uniquely given simpler symmetric tensor which can be obtained by adding the divergence of a suitable superpotential to the canonical energymomentum tensor following from the Fierz-Pauli action. In contrast to the symmetric tensor derived by the Belinfante procedure which involves the second derivatives of the field variables, this expression contains only the field and its first derivatives. It is simpler than the generalized Landau-Lifshitz tensor but both yield the same total quantities since they differ by the divergence of a superpotential. We also discuss the role of the gauge conditions in the proofs of the uniqueness. In the Appendix, the symbolic tensor manipulation software CADABRA is briefly described. It is very effective in obtaining various results which would otherwise require lengthy calculations.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BE - Theoretical physics

OECD FORD branch

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Project

<a href="/en/project/GB14-37086G" target="_blank" >GB14-37086G: Albert Einstein Center for Gravitation and Astrophysics</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2016

Confidentiality

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

Name of the periodical

PHYSICAL REVIEW D

ISSN

2470-0010

e-ISSN

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Volume of the periodical

93

Issue of the periodical within the volume

2

Country of publishing house

US - UNITED STATES

Number of pages

14

Pages from-to

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UT code for WoS article

000367675100006

EID of the result in the Scopus database

2-s2.0-84955443745