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New metric reconstruction scheme for gravitational self-force calculations

New metric reconstruction scheme for gravitational self-force calculations
New metric reconstruction scheme for gravitational self-force calculations
Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating the metric perturbation due to a point particle orbiting a Kerr black hole. Currently, the linear perturbation is obtained with a metric reconstruction procedure that puts it in a “no-string” radiation gauge which is singular on a surface surrounding the central black hole. Calculating dynamical quantities in this gauge involves a subtle procedure of “gauge completion” as well as cancellations of very large numbers. The singularities in the gauge also lead to pathological field equations at second perturbative order. In this paper we re-analyze the point-particle problem in Kerr using the corrector-field reconstruction formalism of Green, Hollands, and Zimmerman (GHZ). We clarify the relationship between the GHZ formalism and previous reconstruction methods, showing that it provides a simple formula for the “gauge completion”. We then use it to develop a new method of computing the metric in a more regular gauge: a Teukolsky puncture scheme. This scheme should ameliorate the problem of large cancellations, and by constructing the linear metric perturbation in a sufficiently regular gauge, it should provide a first step toward second-order selfforce calculations in Kerr. Our methods are developed in generality in Kerr, but we illustrate some key ideas and demonstrate our puncture scheme in the simple setting of a static particle in Minkowski spacetime.
0264-9381
Toomani, Vahid
79b8abb7-4ca2-4824-8c2a-13e0552c3a07
Zimmerman, Peter
4cf73605-e7f0-44f1-ac1f-46eb4f93326a
Spiers, Andrew, Robert Cliford
fc1a647b-1c2e-4685-9903-98ce58e2484a
Hollands, Stefan
40b86265-da22-4798-92fd-64dc4908191f
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Green, Stephen
1956a1c5-2305-4eec-9477-ae3920eaf55a
Toomani, Vahid
79b8abb7-4ca2-4824-8c2a-13e0552c3a07
Zimmerman, Peter
4cf73605-e7f0-44f1-ac1f-46eb4f93326a
Spiers, Andrew, Robert Cliford
fc1a647b-1c2e-4685-9903-98ce58e2484a
Hollands, Stefan
40b86265-da22-4798-92fd-64dc4908191f
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Green, Stephen
1956a1c5-2305-4eec-9477-ae3920eaf55a

Toomani, Vahid, Zimmerman, Peter, Spiers, Andrew, Robert Cliford, Hollands, Stefan, Pound, Adam and Green, Stephen (2021) New metric reconstruction scheme for gravitational self-force calculations. Classical and Quantum Gravity. (doi:10.1088/1361-6382/ac37a5).

Record type: Article

Abstract

Inspirals of stellar-mass objects into massive black holes will be important sources for the space-based gravitational-wave detector LISA. Modelling these systems requires calculating the metric perturbation due to a point particle orbiting a Kerr black hole. Currently, the linear perturbation is obtained with a metric reconstruction procedure that puts it in a “no-string” radiation gauge which is singular on a surface surrounding the central black hole. Calculating dynamical quantities in this gauge involves a subtle procedure of “gauge completion” as well as cancellations of very large numbers. The singularities in the gauge also lead to pathological field equations at second perturbative order. In this paper we re-analyze the point-particle problem in Kerr using the corrector-field reconstruction formalism of Green, Hollands, and Zimmerman (GHZ). We clarify the relationship between the GHZ formalism and previous reconstruction methods, showing that it provides a simple formula for the “gauge completion”. We then use it to develop a new method of computing the metric in a more regular gauge: a Teukolsky puncture scheme. This scheme should ameliorate the problem of large cancellations, and by constructing the linear metric perturbation in a sufficiently regular gauge, it should provide a first step toward second-order selfforce calculations in Kerr. Our methods are developed in generality in Kerr, but we illustrate some key ideas and demonstrate our puncture scheme in the simple setting of a static particle in Minkowski spacetime.

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Accepted/In Press date: 8 November 2021
e-pub ahead of print date: 16 December 2021

Identifiers

Local EPrints ID: 452294
URI: http://eprints.soton.ac.uk/id/eprint/452294
ISSN: 0264-9381
PURE UUID: f4003290-e7bb-43af-a793-a64733b728ff
ORCID for Andrew, Robert Cliford Spiers: ORCID iD orcid.org/0000-0003-0222-7578
ORCID for Adam Pound: ORCID iD orcid.org/0000-0001-9446-0638

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Date deposited: 03 Dec 2021 17:32
Last modified: 17 Mar 2024 03:27

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Contributors

Author: Vahid Toomani
Author: Peter Zimmerman
Author: Stefan Hollands
Author: Adam Pound ORCID iD
Author: Stephen Green

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