Favata, Marc (2001) Energy localization invariance of tidal work in general relativity. Physical Review D, 63 (6). Art. no. 064013. ISSN 05562821. http://resolver.caltech.edu/CaltechAUTHORS:FAVprd01

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Abstract
It is well known that when an external general relativistic (electrictype) tidal field Ejk(t) interacts with the evolving quadrupole moment Ijk(t) of an isolated body the tidal field does work on the body (“tidal work”)—i.e., it transfers energy to the body—at a rate given by the same formula as in Newtonian theory: dW/dt=1/2EjkdIjk/dt. Thorne has posed the following question: In view of the fact that the gravitational interaction energy Eint between the tidal field and the body is ambiguous by an amount ∼EjkIjk, is the tidal work also ambiguous by this amount, and therefore is the formula dW/dt=1/2EjkdIjk/dt only valid unambiguously when integrated over time scales long compared to that for Ijk to change substantially? This paper completes a demonstration that the answer is no; dW/dt is not ambiguous in this way. More specifically, this paper shows that dW/dt is unambiguously given by 1/2EjkdIjk/dt independently of one’s choice of how to localize gravitational energy in general relativity. This is proved by explicitly computing dW/dt using various gravitational stressenergy pseudotensors (Einstein, LandauLifshitz, Møller) as well as Bergmann’s conserved quantities which generalize many of the pseudotensors to include an arbitrary function of position. A discussion is also given of the problem of formulating conservation laws in general relativity and the role played by the various pseudotensors.
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Additional Information:  ©2001 The American Physical Society Received 24 August 2000; published 13 February 2001 I thank Kip Thorne for suggesting this research project and for many insightful discussions as to its solution and the prose of this paper. I also acknowledge Patricia Purdue for useful discussions related to her paper. This research was supported by Caltech, by NSF grant AST9731698, and NASA grant NAG5 6840. 
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Alternative URL:  http://dx.doi.org/10.1103/PhysRevD.63.064013 
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Deposited On:  05 Jan 2006 
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