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The self-consistent gravitational self-force

The self-consistent gravitational self-force
The self-consistent gravitational self-force
I review the problem of motion for small bodies in general relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed. I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body’s past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long time scales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.
1550-7998
024023-[45pp]
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70

Pound, Adam (2010) The self-consistent gravitational self-force. Physical Review D, 81 (2), 024023-[45pp]. (doi:10.1103/PhysRevD.81.024023).

Record type: Article

Abstract

I review the problem of motion for small bodies in general relativity, with an emphasis on developing a self-consistent treatment of the gravitational self-force. An analysis of the various derivations extant in the literature leads me to formulate an asymptotic expansion in which the metric is expanded while a representative worldline is held fixed. I discuss the utility of this expansion for both exact point particles and asymptotically small bodies, contrasting it with a regular expansion in which both the metric and the worldline are expanded. Based on these preliminary analyses, I present a general method of deriving self-consistent equations of motion for arbitrarily structured (sufficiently compact) small bodies. My method utilizes two expansions: an inner expansion that keeps the size of the body fixed, and an outer expansion that lets the body shrink while holding its worldline fixed. By imposing the Lorenz gauge, I express the global solution to the Einstein equation in the outer expansion in terms of an integral over a worldtube of small radius surrounding the body. Appropriate boundary data on the tube are determined from a local-in-space expansion in a buffer region where both the inner and outer expansions are valid. This buffer-region expansion also results in an expression for the self-force in terms of irreducible pieces of the metric perturbation on the worldline. Based on the global solution, these pieces of the perturbation can be written in terms of a tail integral over the body’s past history. This approach can be applied at any order to obtain a self-consistent approximation that is valid on long time scales, both near and far from the small body. I conclude by discussing possible extensions of my method and comparing it to alternative approaches.

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Published date: 20 January 2010
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 339868
URI: http://eprints.soton.ac.uk/id/eprint/339868
ISSN: 1550-7998
PURE UUID: eb6a73ec-2d4d-47b6-986f-0ac57f1dd3e4
ORCID for Adam Pound: ORCID iD orcid.org/0000-0001-9446-0638

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Date deposited: 31 May 2012 15:57
Last modified: 15 Mar 2024 03:41

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