Quadratic quasinormal modes at null infinity on a Schwarzschild spacetime
Quadratic quasinormal modes at null infinity on a Schwarzschild spacetime
The ringdown of perturbed black holes has been studied since the 1970s, but until recently, studies have focused on linear perturbations. There is now burgeoning interest in nonlinear perturbative effects during ringdown. Here, using a hyperboloidal framework, we provide a complete treatment of linear and quadratic quasinormal modes (QNMs and QQNMs) in second-order perturbation theory, in Schwarzschild spacetime. We include novel methods for extracting QNMs and QQNMs amplitudes using a Laplace transform treatment, allowing for the inclusion of arbitrary initial data. We produce both time- and frequency-domain codes. From these codes, we present new results further exploring the unforeseen dependence of QQNMs amplitudes on the parity of the progenitor system, as demonstrated in our letter [Phys. Rev. Lett. 134, 061401 (2025).]. Our numerical results are restricted to perturbations of a Schwarzschild black hole, but our methods extend straightforwardly to the astrophysically realistic case of a Kerr black hole.
Bourg, Patrick
5417cca6-3b5d-45c5-a284-fa41f967870c
Panosso Macedo, Rodrigo
1e42b0b9-2aad-44a1-80cd-efec1ea3ebc5
Spiers, Andrew
246e548b-afc4-491a-8ceb-4a0eb5387131
Leather, Benjamin
f695f9c5-d5c2-48fa-b7c4-cbef9a5919fc
Bonga, Beatrice
6f4ec918-7355-49d5-bc79-960978faa50d
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
26 August 2025
Bourg, Patrick
5417cca6-3b5d-45c5-a284-fa41f967870c
Panosso Macedo, Rodrigo
1e42b0b9-2aad-44a1-80cd-efec1ea3ebc5
Spiers, Andrew
246e548b-afc4-491a-8ceb-4a0eb5387131
Leather, Benjamin
f695f9c5-d5c2-48fa-b7c4-cbef9a5919fc
Bonga, Beatrice
6f4ec918-7355-49d5-bc79-960978faa50d
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Bourg, Patrick, Panosso Macedo, Rodrigo, Spiers, Andrew, Leather, Benjamin, Bonga, Beatrice and Pound, Adam
(2025)
Quadratic quasinormal modes at null infinity on a Schwarzschild spacetime.
Physical Review D, 112, [044049].
(doi:10.1103/fbz4-qsvn).
Abstract
The ringdown of perturbed black holes has been studied since the 1970s, but until recently, studies have focused on linear perturbations. There is now burgeoning interest in nonlinear perturbative effects during ringdown. Here, using a hyperboloidal framework, we provide a complete treatment of linear and quadratic quasinormal modes (QNMs and QQNMs) in second-order perturbation theory, in Schwarzschild spacetime. We include novel methods for extracting QNMs and QQNMs amplitudes using a Laplace transform treatment, allowing for the inclusion of arbitrary initial data. We produce both time- and frequency-domain codes. From these codes, we present new results further exploring the unforeseen dependence of QQNMs amplitudes on the parity of the progenitor system, as demonstrated in our letter [Phys. Rev. Lett. 134, 061401 (2025).]. Our numerical results are restricted to perturbations of a Schwarzschild black hole, but our methods extend straightforwardly to the astrophysically realistic case of a Kerr black hole.
Text
Long_version_QQNM_paper_Schwarzschild
- Accepted Manuscript
More information
Accepted/In Press date: 9 July 2025
Published date: 26 August 2025
Identifiers
Local EPrints ID: 505532
URI: http://eprints.soton.ac.uk/id/eprint/505532
ISSN: 2470-0010
PURE UUID: 80fcd857-9f1b-4d33-9a90-f3137d338043
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Date deposited: 13 Oct 2025 16:50
Last modified: 14 Oct 2025 01:46
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Contributors
Author:
Patrick Bourg
Author:
Rodrigo Panosso Macedo
Author:
Andrew Spiers
Author:
Benjamin Leather
Author:
Beatrice Bonga
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