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

Sam R. Dolan* and Leor Barack†

  • School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom

  • *s.dolan@soton.ac.uk
  • †l.barack@soton.ac.uk
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Phys. Rev. D 83, 024019 – Published 14 January, 2011

DOI: https://doi.org/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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See Also

Self-force via m-mode regularization and 2+1D evolution. II. Scalar-field implementation on Kerr spacetime

Sam R. Dolan, Leor Barack, and Barry Wardell
Phys. Rev. D 84, 084001 (2011)

Self-force via m-mode regularization and 2+1D evolution. III. Gravitational field on Schwarzschild spacetime

Sam R. Dolan and Leor Barack
Phys. Rev. D 87, 084066 (2013)

Article Text

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Outline

Information

Phys. Rev. D 83, 024019– Published 14 January, 2011
  • Received 2 November 2010

© 2011 The American Physical Society

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