Frequency-domain algorithm for the Lorenz-gauge gravitational self-force

Sarp Akcay, Niels Warburton, and Leor Barack
Phys. Rev. D 88, 104009 – Published 12 November 2013

Abstract

State-of-the-art computations of the gravitational self-force (GSF) on massive particles in black hole spacetimes involve numerical evolution of the metric perturbation equations in the time domain, which is computationally very costly. We present here a new strategy based on a frequency-domain treatment of the perturbation equations, which offers considerable computational saving. The essential ingredients of our method are (i) a Fourier-harmonic decomposition of the Lorenz-gauge metric perturbation equations and a numerical solution of the resulting coupled set of ordinary equations with suitable boundary conditions; (ii) a generalized version of the method of extended homogeneous solutions [L. Barack, A. Ori, and N. Sago, Phys. Rev. D 78, 084021 (2008)] used to circumvent the Gibbs phenomenon that would otherwise hamper the convergence of the Fourier mode sum at the particle’s location; (iii) standard mode-sum regularization, which finally yields the physical GSF as a sum over regularized modal contributions. We present a working code that implements this strategy to calculate the Lorenz-gauge GSF along eccentric geodesic orbits around a Schwarzschild black hole. The code is far more efficient than existing time-domain methods; the gain in computation speed (at a given precision) is about an order of magnitude at an eccentricity of 0.2, and up to 3 orders of magnitude for circular or nearly circular orbits. This increased efficiency was crucial in enabling the recently reported calculation of the long-term orbital evolution of an extreme mass ratio inspiral [N. Warburton, S. Akcay, L. Barack, J. R. Gair, and N. Sago, Phys. Rev. D 85, 061501(R) (2012)]. Here we provide full technical details of our method to complement the above report.

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  • Received 23 August 2013

DOI:https://doi.org/10.1103/PhysRevD.88.104009

© 2013 American Physical Society

Authors & Affiliations

Sarp Akcay1, Niels Warburton2, and Leor Barack1

  • 1School of Mathematics, University of Southampton, Southampton SO17 1BJ, United Kingdom
  • 2School of Mathematical Sciences and Complex & Adaptive Systems Laboratory, University College Dublin, Belfield, Dublin 4, Ireland

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Vol. 88, Iss. 10 — 15 November 2013

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