1. Self-force via m-mode regularization and 2 + 1D evolution. III. Gravitational field on Schwarzschild spacetime.
- Author
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Dolan, Sam R. and Barack, Leor
- Subjects
- *
GRAVITATIONAL fields , *MATHEMATICAL regularization , *SCHWARZSCHILD metric , *SPACETIME , *TIME-domain analysis , *QUANTUM perturbations , *SYMMETRY (Physics) - 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, for the case of circular geodesic orbits. 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. [ABSTRACT FROM AUTHOR]
- Published
- 2013
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