Flux-balance laws in scalar self-force theory
Flux-balance laws in scalar self-force theory
The motion of a radiating point particle can be represented by a series of geodesics whose "constants"of motion evolve slowly with time. The evolution of these constants of motion can be determined directly from the self-force equations of motion. In the presence of spacetime symmetries, the situation simplifies; there exist not only constants of motion conjugate to these symmetries, but also conserved currents whose fluxes can be used to determine their evolution. Such a relationship between point-particle motion and fluxes of conserved currents is a flux-balance law. However, there exist constants of motion that are not related to spacetime symmetries, the most notable example of which is the Carter constant in the Kerr spacetime. In this paper, we first present a new approach to flux-balance laws for spacetime symmetries, using the techniques of symplectic currents and symmetry operators, which can also generate more general conserved currents. We then derive flux-balance laws for all constants of motion in the Kerr spacetime, using the fact that the background, geodesic motion is integrable. For simplicity, we restrict derivations in this paper to the scalar self-force problem. While generalizing the discussion in this paper to the gravitational case will be straightforward, there will be additional complications in turning these results into a practical flux-balance law in this case.
Grant, Alexander M.
497961d0-19ca-42dc-b989-8125d7842bfa
Moxon, Jordan
c449db4e-ecb7-415a-aa33-a2317bdab6ae
15 November 2023
Grant, Alexander M.
497961d0-19ca-42dc-b989-8125d7842bfa
Moxon, Jordan
c449db4e-ecb7-415a-aa33-a2317bdab6ae
Grant, Alexander M. and Moxon, Jordan
(2023)
Flux-balance laws in scalar self-force theory.
Physical Review D, 108 (10), [104029].
(doi:10.1103/PhysRevD.108.104029).
Abstract
The motion of a radiating point particle can be represented by a series of geodesics whose "constants"of motion evolve slowly with time. The evolution of these constants of motion can be determined directly from the self-force equations of motion. In the presence of spacetime symmetries, the situation simplifies; there exist not only constants of motion conjugate to these symmetries, but also conserved currents whose fluxes can be used to determine their evolution. Such a relationship between point-particle motion and fluxes of conserved currents is a flux-balance law. However, there exist constants of motion that are not related to spacetime symmetries, the most notable example of which is the Carter constant in the Kerr spacetime. In this paper, we first present a new approach to flux-balance laws for spacetime symmetries, using the techniques of symplectic currents and symmetry operators, which can also generate more general conserved currents. We then derive flux-balance laws for all constants of motion in the Kerr spacetime, using the fact that the background, geodesic motion is integrable. For simplicity, we restrict derivations in this paper to the scalar self-force problem. While generalizing the discussion in this paper to the gravitational case will be straightforward, there will be additional complications in turning these results into a practical flux-balance law in this case.
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flux_balance
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More information
Accepted/In Press date: 12 October 2023
e-pub ahead of print date: 14 November 2023
Published date: 15 November 2023
Additional Information:
Funding Information:
We thank Adam Pound for many valuable discussions, and Éanna Flanagan, David Nichols, and Adam Pound for feedback on an early draft of this work. A. M. G. acknowledges the support of the Royal Society under Grant No. RF\ERE\221005.
Publisher Copyright:
© 2023 American Physical Society.
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Local EPrints ID: 484743
URI: http://eprints.soton.ac.uk/id/eprint/484743
ISSN: 2470-0010
PURE UUID: 38849580-7635-4c14-9e70-34763cc14748
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Date deposited: 21 Nov 2023 17:30
Last modified: 17 Mar 2024 05:56
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Author:
Alexander M. Grant
Author:
Jordan Moxon
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