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Practical, covariant puncture for second-order self-force calculations

Practical, covariant puncture for second-order self-force calculations
Practical, covariant puncture for second-order self-force calculations
Accurately modeling an extreme-mass-ratio inspiral requires knowledge of the second-order gravitational self-force on the inspiraling small object. Recently, numerical puncture schemes have been formulated to calculate this force, and their essential analytical ingredients have been derived from first principles. However, the “puncture,” a local representation of the small object’s self-field, in each of these schemes has been presented only in a local coordinate system centered on the small object, while a numerical implementation will require the puncture in coordinates covering the entire numerical domain. In this paper we provide an explicit covariant self-field as a local expansion in terms of Synge’s world function. The self-field is written in the Lorenz gauge, in an arbitrary vacuum background, and in forms suitable for both self-consistent and Gralla-Wald-type representations of the object’s trajectory. We illustrate the local expansion’s utility by sketching the procedure of constructing from it a numerically practical puncture in any chosen coordinate system.
1550-7998
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Miller, Jeremy
35ef0e88-726a-444d-b502-1c2b828fa80d
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Miller, Jeremy
35ef0e88-726a-444d-b502-1c2b828fa80d

Pound, Adam and Miller, Jeremy (2014) Practical, covariant puncture for second-order self-force calculations. Physical Review D. (doi:10.1103/PhysRevD.89.104020).

Record type: Article

Abstract

Accurately modeling an extreme-mass-ratio inspiral requires knowledge of the second-order gravitational self-force on the inspiraling small object. Recently, numerical puncture schemes have been formulated to calculate this force, and their essential analytical ingredients have been derived from first principles. However, the “puncture,” a local representation of the small object’s self-field, in each of these schemes has been presented only in a local coordinate system centered on the small object, while a numerical implementation will require the puncture in coordinates covering the entire numerical domain. In this paper we provide an explicit covariant self-field as a local expansion in terms of Synge’s world function. The self-field is written in the Lorenz gauge, in an arbitrary vacuum background, and in forms suitable for both self-consistent and Gralla-Wald-type representations of the object’s trajectory. We illustrate the local expansion’s utility by sketching the procedure of constructing from it a numerically practical puncture in any chosen coordinate system.

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e-pub ahead of print date: 13 May 2014
Published date: 15 May 2014
Organisations: Mathematical Sciences, Applied Mathematics

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Local EPrints ID: 411257
URI: https://eprints.soton.ac.uk/id/eprint/411257
ISSN: 1550-7998
PURE UUID: 26c32909-193f-4a91-a159-8a83cc06a32f

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Date deposited: 16 Jun 2017 16:31
Last modified: 28 Oct 2019 18:53

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Author: Adam Pound
Author: Jeremy Miller

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