### Abstract

It is well known that when an external general relativistic (electric-type) tidal field £,-(/) interacts with the evolving quadrupole moment Zy(0 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: d\Vldt = - £dljkldt. Thorne has posed the following question: In view of the fact that the gravitational interaction energy £int between the tidal field and the body is ambiguous by an amount ~Bj{L, is the tidal work also ambiguous by this amount, and therefore is the formula d\V/dt= -2£jkdZjk/dt only valid unambiguously when integrated over time scales long compared to that for Z, to change substantially? This paper completes a demonstration that the answer is no; dWIdt is not ambiguous in this way. More specifically, this paper shows that dWIdt is unambiguously given by -jtdlldt 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, M511er) 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.

Original language | English |
---|---|

Article number | 064013 |

Journal | Physical Review D |

Volume | 63 |

Issue number | 6 |

DOIs | |

State | Published - 1 Dec 2001 |

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*Physical Review D*, vol. 63, no. 6, 064013. https://doi.org/10.1103/PhysRevD.63.064013

**Energy localization invariance of tidal work in general relativity.** / Favata, Marc.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Energy localization invariance of tidal work in general relativity

AU - Favata, Marc

PY - 2001/12/1

Y1 - 2001/12/1

N2 - It is well known that when an external general relativistic (electric-type) tidal field £,-(/) interacts with the evolving quadrupole moment Zy(0 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: d\Vldt = - £dljkldt. Thorne has posed the following question: In view of the fact that the gravitational interaction energy £int between the tidal field and the body is ambiguous by an amount ~Bj{L, is the tidal work also ambiguous by this amount, and therefore is the formula d\V/dt= -2£jkdZjk/dt only valid unambiguously when integrated over time scales long compared to that for Z, to change substantially? This paper completes a demonstration that the answer is no; dWIdt is not ambiguous in this way. More specifically, this paper shows that dWIdt is unambiguously given by -jtdlldt 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, M511er) 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.

AB - It is well known that when an external general relativistic (electric-type) tidal field £,-(/) interacts with the evolving quadrupole moment Zy(0 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: d\Vldt = - £dljkldt. Thorne has posed the following question: In view of the fact that the gravitational interaction energy £int between the tidal field and the body is ambiguous by an amount ~Bj{L, is the tidal work also ambiguous by this amount, and therefore is the formula d\V/dt= -2£jkdZjk/dt only valid unambiguously when integrated over time scales long compared to that for Z, to change substantially? This paper completes a demonstration that the answer is no; dWIdt is not ambiguous in this way. More specifically, this paper shows that dWIdt is unambiguously given by -jtdlldt 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, M511er) 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.

UR - http://www.scopus.com/inward/record.url?scp=33750814168&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.63.064013

DO - 10.1103/PhysRevD.63.064013

M3 - Article

VL - 63

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 6

M1 - 064013

ER -