2010/10/25 by Sam R. Dolan, Leor Barack
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Pulsars and Gravitational Waves Research #astro-ph.HE #gr-qc
paper · pdf · doi:10.1103/physrevd.83.024019
published as Phys.Rev.D83:024019,2011 · 46 pages, 18 figures, 8 tables
arxiv created 2010/10/25 · openalex publication_date 2011/01/14 · arxiv updated 2011/02/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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^\ensuremath-n for even n and as m^\ensuremath-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.