Favata, Marc (2001) Energy localization invariance of tidal work in general relativity. Physical Review D, 63 (6). Art. no. 064013. ISSN 0556-2821. http://resolver.caltech.edu/CaltechAUTHORS:FAVprd01
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It is well known that when an external general relativistic (electric-type) 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 stress-energy pseudotensors (Einstein, Landau-Lifshitz, 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.
|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 AST-9731698, and NASA grant NAG5 6840.|
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|Deposited On:||05 Jan 2006|
|Last Modified:||26 Dec 2012 08:43|
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