Self-force via m-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
Self-force via m-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
This is the third in a series of papers aimed at developing a practical time-domain method for self-force calculations in Kerr spacetime. The key elements of the method are (i) removal of a singular part of the perturbation field with a suitable analytic "puncture", (ii) decomposition of the perturbation equations in azimuthal (m-)modes, taking advantage of the axial symmetry of the Kerr background, (iii) numerical evolution of the individual $m$-modes in 2+1-dimensions with a finite difference scheme, and (iv) reconstruction of the local self-force from the mode sum. Here we report a first implementation of the method to compute the gravitational self-force. We work in the Lorenz gauge, solving directly for the metric perturbation in 2+1-dimensions. The modes m=0,1$ contain nonradiative pieces, whose time-domain evolution is hampered by certain gauge instabilities. We study this problem in detail and propose ways around it. In the current work we use the Schwarzschild geometry as a platform for development; in a forthcoming paper-the fourth in the series-we apply our method to the gravitational self-force in Kerr geometry.
Dolan, Sam R.
ee9c2137-170a-4942-9655-862a98f389c2
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Dolan, Sam R.
ee9c2137-170a-4942-9655-862a98f389c2
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Dolan, Sam R. and Barack, Leor
(2013)
Self-force via m-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime.
Pre-print.
(doi:10.1103/PhysRevD.87.084066).
(Submitted)
Abstract
This is the third in a series of papers aimed at developing a practical time-domain method for self-force calculations in Kerr spacetime. The key elements of the method are (i) removal of a singular part of the perturbation field with a suitable analytic "puncture", (ii) decomposition of the perturbation equations in azimuthal (m-)modes, taking advantage of the axial symmetry of the Kerr background, (iii) numerical evolution of the individual $m$-modes in 2+1-dimensions with a finite difference scheme, and (iv) reconstruction of the local self-force from the mode sum. Here we report a first implementation of the method to compute the gravitational self-force. We work in the Lorenz gauge, solving directly for the metric perturbation in 2+1-dimensions. The modes m=0,1$ contain nonradiative pieces, whose time-domain evolution is hampered by certain gauge instabilities. We study this problem in detail and propose ways around it. In the current work we use the Schwarzschild geometry as a platform for development; in a forthcoming paper-the fourth in the series-we apply our method to the gravitational self-force in Kerr geometry.
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Submitted date: 2013
Additional Information:
arXiv:1211.4586
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Applied Mathematics
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Local EPrints ID: 347767
URI: http://eprints.soton.ac.uk/id/eprint/347767
PURE UUID: 4257daf6-9c1a-4499-8b70-2692f468f764
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Date deposited: 30 Jan 2013 14:07
Last modified: 15 Mar 2024 03:21
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Author:
Sam R. Dolan
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