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

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

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.

1-22

Akcay, Sarp

dcb16394-6b37-43a3-90ca-925458bfd668

Warburton, Niels

03087256-aa46-485d-8ac0-da73dd66ed61

Barack, Leor

f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

12 November 2013

Akcay, Sarp

dcb16394-6b37-43a3-90ca-925458bfd668

Warburton, Niels

03087256-aa46-485d-8ac0-da73dd66ed61

Barack, Leor

f08e66d4-c2f7-4f2f-91b8-f2c4230d0298

Akcay, Sarp, Warburton, Niels and Barack, Leor
(2013)
Frequency-domain algorithm for the Lorenz-gauge gravitational self-force.
*Physical Review D*, 88 (10), .
(doi:10.1103/PhysRevD.88.104009).

## 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.

Other

** PhysRevD.88.104009
- Version of Record**
Available under License Other.

## More information

Published date: 12 November 2013

Organisations:
Mathematical Sciences

## Identifiers

Local EPrints ID: 369414

URI: https://eprints.soton.ac.uk/id/eprint/369414

ISSN: 1550-7998

PURE UUID: cc49ec46-0b1c-4196-8a7d-5389605b1553

## Catalogue record

Date deposited: 25 Sep 2014 13:57

Last modified: 17 Jul 2017 21:57

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## Contributors

Author:
Sarp Akcay

Author:
Niels Warburton

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