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Note on positive-definiteness of the energy of the gravitational field

Arnowitt, R. and Deser, S. and Misner, C. W. (1960) Note on positive-definiteness of the energy of the gravitational field. Annals of Physics, 11 (1). pp. 116-121. ISSN 0003-4916. http://resolver.caltech.edu/CaltechAUTHORS:20181120-133838985

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Abstract

The energy of the gravitational field is shown to be positive-definite for the case where initially (a) the spatial metric g_(ij) can be made isotropic and (b) the second fundamental form K_(ij) ≡ -(-g^(00)^(-12)Γ^0_(ij) (which is essentially ) is arbitrary apart from the coordinate condition K ≡ K_(ij)^3g_(ij) = 0 defining the initial t = const. surface. Physically, this situation corresponds to no wave excitations initially in g_(ij), but arbitrary ones in K_(ij). More precisely, the two canonical coordinates of the field are initially zero, while their conjugate momenta are arbitrary. The total energy of the system is also positive when sources with positive energies are coupled to the gravitational field. Some aspects of the general problem (where g_(ij) is also arbitrary initially) are discussed.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1016/0003-4916(60)90129-9DOIArticle
ORCID:
AuthorORCID
Deser, S.0000-0001-9285-9434
Additional Information:© 1960 Published by Elsevier. Received 28 April 1960. Research supported in part by the United States Air Force under Contract No. AF 33(616)-5598 monitored by the Aeronautical Research Laboratory, WADD and Contract No. AF 49(638)-636 of the Air Force Office of Scientific Research. Research supported in part by the National Science Foundation and Air Force Office of Scientific Research under Contract No. AF 49(638)-636.
Funders:
Funding AgencyGrant Number
Air Force Office of Scientific Research (AFOSR)AF 33(616)-5598
Air Force Office of Scientific Research (AFOSR)AF 49(638)-636
NSFUNSPECIFIED
Alfred P. Sloan FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20181120-133838985
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20181120-133838985
Official Citation:R Arnowitt, S Deser, C.W Misner, Note on positive-definiteness of the energy of the gravitational field, Annals of Physics, Volume 11, Issue 1, 1960, Pages 116-121, ISSN 0003-4916, https://doi.org/10.1016/0003-4916(60)90129-9. (http://www.sciencedirect.com/science/article/pii/0003491660901299)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:91078
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:20 Nov 2018 22:49
Last Modified:20 Nov 2018 22:49

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