Second-order Teukolsky formalism in Kerr spacetime: formulation and nonlinear source
Second-order Teukolsky formalism in Kerr spacetime: formulation and nonlinear source
To fully exploit the capabilities of next-generation gravitational wave detectors, we need to significantly improve the accuracy of our models of gravitational-wave-emitting systems. This paper focuses on one way of doing so: by taking black hole perturbation theory to second perturbative order. Such calculations are critical for the development of nonlinear ringdown models and of gravitational self-force models of extreme-mass-ratio inspirals. In the most astrophysically realistic case of a Kerr background, a second-order Teukolsky equation presents the most viable avenue for calculating second-order perturbations. Motivated by this, we analyze two second-order Teukolsky formalisms and advocate for the one that is well-behaved for gravitational self-force calculations and which meshes naturally with recent metric reconstruction methods due to Green, Hollands, and Zimmerman [CQG 37, 075001 (2020)] and others. Our main result is an expression for the nonlinear source term in the second-order field equation; we make this available, along with other useful tools, in an accompanying Mathematica notebook. Using our expression for the source, we also show that infrared divergences at second order can be evaded by adopting a Bondi-Sachs gauge.
Spiers, Andrew
fc1a647b-1c2e-4685-9903-98ce58e2484a
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Moxon, Jordan
0591fadd-e3ba-43ee-81da-693d575ef307
15 September 2023
Spiers, Andrew
fc1a647b-1c2e-4685-9903-98ce58e2484a
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Moxon, Jordan
0591fadd-e3ba-43ee-81da-693d575ef307
Spiers, Andrew, Pound, Adam and Moxon, Jordan
(2023)
Second-order Teukolsky formalism in Kerr spacetime: formulation and nonlinear source.
Physical Review D, 108 (6), [064002].
(doi:10.1103/PhysRevD.108.064002).
Abstract
To fully exploit the capabilities of next-generation gravitational wave detectors, we need to significantly improve the accuracy of our models of gravitational-wave-emitting systems. This paper focuses on one way of doing so: by taking black hole perturbation theory to second perturbative order. Such calculations are critical for the development of nonlinear ringdown models and of gravitational self-force models of extreme-mass-ratio inspirals. In the most astrophysically realistic case of a Kerr background, a second-order Teukolsky equation presents the most viable avenue for calculating second-order perturbations. Motivated by this, we analyze two second-order Teukolsky formalisms and advocate for the one that is well-behaved for gravitational self-force calculations and which meshes naturally with recent metric reconstruction methods due to Green, Hollands, and Zimmerman [CQG 37, 075001 (2020)] and others. Our main result is an expression for the nonlinear source term in the second-order field equation; we make this available, along with other useful tools, in an accompanying Mathematica notebook. Using our expression for the source, we also show that infrared divergences at second order can be evaded by adopting a Bondi-Sachs gauge.
Text
2nd_order_Teukolsky_equation
- Accepted Manuscript
More information
Accepted/In Press date: 11 August 2023
e-pub ahead of print date: 1 September 2023
Published date: 15 September 2023
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Funding Information:
We thank Beatrice Bonga and Nicholas Loutrel for independently cross-checking the results in Appendix . We also thank Leor Barack, Eanna Flanagan, and Barry Wardell for helpful discussions. A. P. acknowledges the support of a Royal Society University Research Fellowship and associated awards, and A. P. and A. S. specifically acknowledge the support of a Royal Society University Research Fellowship Enhancement Award. A. S. additionally acknowledges partial support from the STFC Consolidated Grant No. ST/V005596/1.
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© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
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Local EPrints ID: 481302
URI: http://eprints.soton.ac.uk/id/eprint/481302
ISSN: 2470-0010
PURE UUID: 197ffde6-c6c0-40dd-9e04-ed6f6b9b7b9c
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Date deposited: 22 Aug 2023 16:54
Last modified: 18 Mar 2024 03:20
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Jordan Moxon
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