Hyperboloidal method for frequency-domain self-force calculations
Hyperboloidal method for frequency-domain self-force calculations
Gravitational self-force theory is the leading approach for modeling gravitational wave emission from small mass-ratio compact binaries. This method perturbatively expands the metric of the binary in powers of the mass ratio. The source for the perturbations depends on the orbital configuration, calculational approach, and the order of the perturbative expansion. These sources fall into three broad classes: (i) distributional, (ii) worldtube, and (iii) unbounded support. The latter, in particular, is important for emerging second-order (in the mass ratio) calculations. Traditional frequency domain approaches employ the variation of parameters method and compute the perturbation on standard time slices with numerical boundary conditions supplied at finite radius from series expansions of the asymptotic behavior. This approach has been very successful, but the boundary conditions calculations are tedious, and the approach is not well suited to unbounded sources where homogeneous solutions must be computed at all radii. This work develops an alternative approach where hyperboloidal slices foliate the spacetime, and compactifying coordinates simplify the boundary treatment. We implement this approach with a multidomain spectral solver with analytic mesh refinement and use the scalar-field self-force on circular orbits around a Schwarzschild black hole as an example problem. The method works efficiently for all three source classes encountered in self-force calculations and has distinct advantages over the traditional approach. For example, our code efficiently computes the perturbation for orbits with extremely large orbital radii (rp>105M) or modes with very high spherical harmonic mode index (?≥100). Our results indicate that hyperboloidal methods can play an essential role in self-force calculations.
104033-1 - 104033-28
Panosso Macedo, Rodrigo
8f176eb4-ca20-492b-a41e-e78d47d6fefe
Leather, Benjamin
89954fe0-9453-4dc5-8280-ca587693b3d2
Warburton, Niels
03087256-aa46-485d-8ac0-da73dd66ed61
Wardell, Barry
70b41899-32ac-4585-888b-aaf28fd70ad5
Zenginglu, Anil
2bc06c76-963f-49a0-84f4-04f9ff9d9913
15 May 2022
Panosso Macedo, Rodrigo
8f176eb4-ca20-492b-a41e-e78d47d6fefe
Leather, Benjamin
89954fe0-9453-4dc5-8280-ca587693b3d2
Warburton, Niels
03087256-aa46-485d-8ac0-da73dd66ed61
Wardell, Barry
70b41899-32ac-4585-888b-aaf28fd70ad5
Zenginglu, Anil
2bc06c76-963f-49a0-84f4-04f9ff9d9913
Panosso Macedo, Rodrigo, Leather, Benjamin, Warburton, Niels, Wardell, Barry and Zenginglu, Anil
(2022)
Hyperboloidal method for frequency-domain self-force calculations.
Physical Review D, 105 (104033), , [104033].
(doi:10.1103/PhysRevD.105.104033).
Abstract
Gravitational self-force theory is the leading approach for modeling gravitational wave emission from small mass-ratio compact binaries. This method perturbatively expands the metric of the binary in powers of the mass ratio. The source for the perturbations depends on the orbital configuration, calculational approach, and the order of the perturbative expansion. These sources fall into three broad classes: (i) distributional, (ii) worldtube, and (iii) unbounded support. The latter, in particular, is important for emerging second-order (in the mass ratio) calculations. Traditional frequency domain approaches employ the variation of parameters method and compute the perturbation on standard time slices with numerical boundary conditions supplied at finite radius from series expansions of the asymptotic behavior. This approach has been very successful, but the boundary conditions calculations are tedious, and the approach is not well suited to unbounded sources where homogeneous solutions must be computed at all radii. This work develops an alternative approach where hyperboloidal slices foliate the spacetime, and compactifying coordinates simplify the boundary treatment. We implement this approach with a multidomain spectral solver with analytic mesh refinement and use the scalar-field self-force on circular orbits around a Schwarzschild black hole as an example problem. The method works efficiently for all three source classes encountered in self-force calculations and has distinct advantages over the traditional approach. For example, our code efficiently computes the perturbation for orbits with extremely large orbital radii (rp>105M) or modes with very high spherical harmonic mode index (?≥100). Our results indicate that hyperboloidal methods can play an essential role in self-force calculations.
Text
2202.01794
- Accepted Manuscript
More information
Accepted/In Press date: 14 April 2022
Published date: 15 May 2022
Additional Information:
Funding Information:
R. P. M. acknowledges financial support provided by the STFC Grant No. ST/V000551/1, COST Action CA16104 via the Short Term Scientific Mission grant, and European Research Council Grant No. ERC-2014-StG 639022-NewNGR “New frontiers in numerical general relativity.” N. W. acknowledges support from a Royal Society—Science Foundation Ireland University Research Fellowship via Grants No. UF160093 and No. RGF\R1\180022. This work makes use of the Black Hole Perturbation Toolkit .
Publisher Copyright:
© 2022 American Physical Society.
Identifiers
Local EPrints ID: 457605
URI: http://eprints.soton.ac.uk/id/eprint/457605
ISSN: 2470-0029
PURE UUID: 9f8860d9-ae6b-4d0c-9f7c-191b548a7a4d
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Date deposited: 14 Jun 2022 16:33
Last modified: 17 Mar 2024 04:09
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Contributors
Author:
Benjamin Leather
Author:
Niels Warburton
Author:
Barry Wardell
Author:
Anil Zenginglu
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