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Self force via m-mode regularization and 2+1D evolution: foundations and a scalar-field implementation on Schwarzschild

Self force via m-mode regularization and 2+1D evolution: foundations and a scalar-field implementation on Schwarzschild
Self force via m-mode regularization and 2+1D evolution: foundations and a scalar-field implementation on Schwarzschild
To model the radiative evolution of extreme mass-ratio binary inspirals (a key target of the LISA mission), the community needs efficient methods for computation of the gravitational self-force (SF) on the Kerr spacetime. Here we further develop a practical “m-mode regularization” scheme for SF calculations, and give the details of a first implementation. The key steps in the method are (i) removal of a singular part of the perturbation field with a suitable “puncture” to leave a sufficiently regular residual within a finite worldtube surrounding the particle’s worldline, (ii) decomposition in azimuthal (m) modes, (iii) numerical evolution of the m modes in 2+1D with a finite-difference scheme, and (iv) reconstruction of the SF from the mode sum. The method relies on a judicious choice of puncture, based on the Detweiler-Whiting decomposition. We give a working definition for the “order” of the puncture, and show how it determines the convergence rate of the m-mode sum. The dissipative piece of the SF displays an exponentially convergent mode sum, while the m-mode sum for the conservative piece converges with a power law. In the latter case, the individual modal contributions fall off at large m as m-n for even n and as m-n+1 for odd n, where n is the puncture order. We describe an m-mode implementation with a 4th-order puncture to compute the scalar-field SF along circular geodesics on Schwarzschild. In a forthcoming companion paper we extend the calculation to the Kerr spacetime
1550-7998
024019-[31pp]
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Dolan, Sam
61aa8fdf-96be-4f31-826f-4982a0792eda
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Dolan, Sam
61aa8fdf-96be-4f31-826f-4982a0792eda

Barack, Leor and Dolan, Sam (2011) Self force via m-mode regularization and 2+1D evolution: foundations and a scalar-field implementation on Schwarzschild. Physical Review D, 83 (2), 024019-[31pp]. (doi:10.1103/PhysRevD.83.024019).

Record type: Article

Abstract

To model the radiative evolution of extreme mass-ratio binary inspirals (a key target of the LISA mission), the community needs efficient methods for computation of the gravitational self-force (SF) on the Kerr spacetime. Here we further develop a practical “m-mode regularization” scheme for SF calculations, and give the details of a first implementation. The key steps in the method are (i) removal of a singular part of the perturbation field with a suitable “puncture” to leave a sufficiently regular residual within a finite worldtube surrounding the particle’s worldline, (ii) decomposition in azimuthal (m) modes, (iii) numerical evolution of the m modes in 2+1D with a finite-difference scheme, and (iv) reconstruction of the SF from the mode sum. The method relies on a judicious choice of puncture, based on the Detweiler-Whiting decomposition. We give a working definition for the “order” of the puncture, and show how it determines the convergence rate of the m-mode sum. The dissipative piece of the SF displays an exponentially convergent mode sum, while the m-mode sum for the conservative piece converges with a power law. In the latter case, the individual modal contributions fall off at large m as m-n for even n and as m-n+1 for odd n, where n is the puncture order. We describe an m-mode implementation with a 4th-order puncture to compute the scalar-field SF along circular geodesics on Schwarzschild. In a forthcoming companion paper we extend the calculation to the Kerr spacetime

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Published date: January 2011

Identifiers

Local EPrints ID: 173675
URI: https://eprints.soton.ac.uk/id/eprint/173675
ISSN: 1550-7998
PURE UUID: bbc1dfce-7087-4b8b-aa1c-8707ad7a58fe
ORCID for Leor Barack: ORCID iD orcid.org/0000-0003-4742-9413

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Date deposited: 08 Feb 2011 08:38
Last modified: 10 Sep 2019 00:44

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