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

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).

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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Contributors

Author: Leor Barack

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