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S. Borhanian, K. G. Arun, H. P. Pfeiffer, and B. S. Sathyaprakash, Comparison of post-Newtonian mode amplitudes with numerical relativity simulations of binary black holes, Class. Quant. Grav. 37
Original
1901
Earlier work this paper cites.
M. Giesler, M. Isi, M. A. Scheel, and S. Teukolsky, Black Hole Ringdown: The Importance of Overtones, Phys. Rev. X 9
Original
1903
Earlier work this paper cites.
M. Boyle et al. , The SXS Collaboration catalog of binary black hole simulations, Class. Quant. Grav. 36
Original
1904
Earlier work this paper cites.
M. Isi, M. Giesler, W. M. Farr, M. A. Scheel, and S. A. Teukolsky, Testing the no-hair theorem with GW150914, Phys. Rev. Lett. 123
Original
1905
Earlier work this paper cites.
L. C. Stein, qnm: A Python package for calculating Kerr quasinormal modes, separation constants, and spherical-spheroidal mixing coefficients, J. Open Source Softw. 4
Original
1908
Earlier work this paper cites.
S. Bhagwat, X. J. Forteza, P. Pani, and V. Ferrari, Ringdown overtones, black hole spectroscopy, and no-hair theorem tests, Phys. Rev. D 101
Original
1910
Earlier work this paper cites.
I. Ota and C. Chirenti, Overtones or higher harmonics? Prospects for testing the no-hair theorem with gravitational wave detections, Phys. Rev. D 101
Original
1911
Earlier work this paper cites.
M. Maggiore et al. , Science Case for the Einstein Telescope, JCAP 03
Original
1912
Earlier work this paper cites.
T. Regge and J. A. Wheeler, Stability of a Schwarzschild singularity, Phys. Rev. 108
1957
Earlier work this paper cites.
R. Penrose, Gravitational collapse: The role of general relativity, Riv. Nuovo Cim. 1
1969
Earlier work this paper cites.
F. J. Zerilli, Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics, Phys. Rev. D 2
1970
Earlier work this paper cites.
S. A. Teukolsky, Perturbations of a rotating black hole. 1. Fundamental equations for gravitational electromagnetic and neutrino field perturbations, Astrophys. J. 185
1973
Earlier work this paper cites.
E. W. Leaver, Spectral decomposition of the perturbation response of the Schwarzschild geometry, Phys. Rev. D 34
1986
Earlier work this paper cites.
M. Campanelli and C. O. Lousto, Second order gauge invariant gravitational perturbations of a Kerr black hole, Phys. Rev. D 59
1999
Earlier work this paper cites.
R. J. Gleiser, C. O. Nicasio, R. H. Price, and J. Pullin, Gravitational radiation from Schwarzschild black holes: The Second order perturbation formalism, Phys. Rept. 325
2000
Earlier work this paper cites.
H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselaers, and E. Herlt, Exact solutions of Einstein’s field equations , Cambridge Monographs on Mathematical Physics (Cambridge Univ. Press, Cambridge, 2003)
2003
Earlier work this paper cites.

Similar

G. B. Cook, Aspects of multimode Kerr ringdown fitting, Phys. Rev. D 102
Original
2004
Cited alongside, same era.
X. Jiménez Forteza, S. Bhagwat, P. Pani, and V. Ferrari, Spectroscopy of binary black hole ringdown using overtones and angular modes, Phys. Rev. D 102
Original
2005
Cited alongside, same era.
K. Ioka and H. Nakano, Second and higher-order quasi-normal modes in binary black hole mergers, Phys. Rev. D 76
Original
2007
Cited alongside, same era.
H. Nakano and K. Ioka, Second Order Quasi-Normal Mode of the Schwarzschild Black Hole, Phys. Rev. D 76
Original
2007
Cited alongside, same era.
K. Mitman, J. Moxon, M. A. Scheel, S. A. Teukolsky, M. Boyle, N. Deppe, L. E. Kidder, and W. Throwe, Computation of displacement and spin gravitational memory in numerical relativity, Phys. Rev. D 102

Then

L. Blanchet, Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Rel. 17
Original
2014
Later among the works it cites.
S. A. Teukolsky, The Kerr Metric, Class. Quant. Grav. 32
Original
2015
Later among the works it cites.
E. Berti, A. Sesana, E. Barausse, V. Cardoso, and K. Belczynski, Spectroscopy of Kerr black holes with Earth- and space-based interferometers, Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.
L. London, D. Shoemaker, and J. Healy, Modeling ringdown: Beyond the fundamental quasinormal modes, Phys. Rev. D 90
Original
2016
Later among the works it cites.
B. P. Abbott et al. (LIGO Scientific, Virgo), GW150914: First results from the search for binary black hole coalescence with Advanced LIGO, Phys. Rev. D 93

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2022

Nonlinearities in Black Hole Ringdowns

Mitman, Keefe, Lagos, Macarena, Stein, Leo C. et al.

Understand

The gravitational wave strain emitted by a perturbed black hole (BH) ringing down is typically modeled analytically using first-order BH perturbation theory.

In this Letter we show that second-order effects are necessary for modeling ringdowns from BH merger simulations.
Focusing on the strain's $(\ell,m)=(4,4)$ angular harmonic, we show the presence of a quadratic effect across a range of binary BH mass ratios that agrees with theoretical expectations.
We find that the quadratic $(4,4)$ mode's amplitude exhibits quadratic scaling with the fundamental $(2,2)$ mode -- its parent mode.

Built on

S. Borhanian, K. G. Arun, H. P. Pfeiffer, and B. S. Sathyaprakash, Comparison of post-Newtonian mode amplitudes with numerical relativity simulations of binary black holes, Class. Quant. Grav. 37
Original
1901
Earlier work this paper cites.
M. Giesler, M. Isi, M. A. Scheel, and S. Teukolsky, Black Hole Ringdown: The Importance of Overtones, Phys. Rev. X 9
Original
1903
Earlier work this paper cites.
M. Boyle et al. , The SXS Collaboration catalog of binary black hole simulations, Class. Quant. Grav. 36
Original
1904
Earlier work this paper cites.
M. Isi, M. Giesler, W. M. Farr, M. A. Scheel, and S. A. Teukolsky, Testing the no-hair theorem with GW150914, Phys. Rev. Lett. 123
Original
1905
Earlier work this paper cites.
L. C. Stein, qnm: A Python package for calculating Kerr quasinormal modes, separation constants, and spherical-spheroidal mixing coefficients, J. Open Source Softw. 4
Original
1908
Earlier work this paper cites.
S. Bhagwat, X. J. Forteza, P. Pani, and V. Ferrari, Ringdown overtones, black hole spectroscopy, and no-hair theorem tests, Phys. Rev. D 101
Original
1910
Earlier work this paper cites.
I. Ota and C. Chirenti, Overtones or higher harmonics? Prospects for testing the no-hair theorem with gravitational wave detections, Phys. Rev. D 101
Original
1911
Earlier work this paper cites.
M. Maggiore et al. , Science Case for the Einstein Telescope, JCAP 03
Original
1912
Earlier work this paper cites.
T. Regge and J. A. Wheeler, Stability of a Schwarzschild singularity, Phys. Rev. 108
1957
Earlier work this paper cites.
R. Penrose, Gravitational collapse: The role of general relativity, Riv. Nuovo Cim. 1
1969
Earlier work this paper cites.
F. J. Zerilli, Gravitational field of a particle falling in a schwarzschild geometry analyzed in tensor harmonics, Phys. Rev. D 2
1970
Earlier work this paper cites.
S. A. Teukolsky, Perturbations of a rotating black hole. 1. Fundamental equations for gravitational electromagnetic and neutrino field perturbations, Astrophys. J. 185
1973
Earlier work this paper cites.
E. W. Leaver, Spectral decomposition of the perturbation response of the Schwarzschild geometry, Phys. Rev. D 34
1986
Earlier work this paper cites.
M. Campanelli and C. O. Lousto, Second order gauge invariant gravitational perturbations of a Kerr black hole, Phys. Rev. D 59
1999
Earlier work this paper cites.
R. J. Gleiser, C. O. Nicasio, R. H. Price, and J. Pullin, Gravitational radiation from Schwarzschild black holes: The Second order perturbation formalism, Phys. Rept. 325
2000
Earlier work this paper cites.
H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselaers, and E. Herlt, Exact solutions of Einstein’s field equations , Cambridge Monographs on Mathematical Physics (Cambridge Univ. Press, Cambridge, 2003)
2003
Earlier work this paper cites.

Similar

G. B. Cook, Aspects of multimode Kerr ringdown fitting, Phys. Rev. D 102
Original
2004
Cited alongside, same era.
X. Jiménez Forteza, S. Bhagwat, P. Pani, and V. Ferrari, Spectroscopy of binary black hole ringdown using overtones and angular modes, Phys. Rev. D 102
Original
2005
Cited alongside, same era.
K. Ioka and H. Nakano, Second and higher-order quasi-normal modes in binary black hole mergers, Phys. Rev. D 76
Original
2007
Cited alongside, same era.
H. Nakano and K. Ioka, Second Order Quasi-Normal Mode of the Schwarzschild Black Hole, Phys. Rev. D 76
Original
2007
Cited alongside, same era.
K. Mitman, J. Moxon, M. A. Scheel, S. A. Teukolsky, M. Boyle, N. Deppe, L. E. Kidder, and W. Throwe, Computation of displacement and spin gravitational memory in numerical relativity, Phys. Rev. D 102

Then

L. Blanchet, Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Rel. 17
Original
2014
Later among the works it cites.
S. A. Teukolsky, The Kerr Metric, Class. Quant. Grav. 32
Original
2015
Later among the works it cites.
E. Berti, A. Sesana, E. Barausse, V. Cardoso, and K. Belczynski, Spectroscopy of Kerr black holes with Earth- and space-based interferometers, Phys. Rev. Lett. 117
Original
2016
Later among the works it cites.
L. London, D. Shoemaker, and J. Healy, Modeling ringdown: Beyond the fundamental quasinormal modes, Phys. Rev. D 90
Original
2016
Later among the works it cites.
B. P. Abbott et al. (LIGO Scientific, Virgo), GW150914: First results from the search for binary black hole coalescence with Advanced LIGO, Phys. Rev. D 93

Beyond the bibliography

alphaXiv searches the wider corpus for related work and actual follow-ups.

Open on alphaXiv

alphaXiv is searching for related work…

Original

2007

Cited alongside, same era.

J. Moxon, M. A. Scheel, and S. A. Teukolsky, Improved Cauchy-characteristic evolution system for high-precision numerical relativity waveforms, Phys. Rev. D 102

Original

2007

Cited alongside, same era.

S. Okuzumi, K. Ioka, and M.-a. Sakagami, Possible Discovery of Nonlinear Tail and Quasinormal Modes in Black Hole Ringdown, Phys. Rev. D 77

Original

2008

Cited alongside, same era.

N. Loutrel, J. L. Ripley, E. Giorgi, and F. Pretorius, Second Order Perturbations of Kerr Black Holes: Reconstruction of the Metric, Phys. Rev. D 103

Original

2008

Cited alongside, same era.

J. B. Griffiths and J. Podolsky, Exact Space-Times in Einstein’s General Relativity , Cambridge Monographs on Mathematical Physics (Cambridge University Press, Cambridge, 2009)

2009

Cited alongside, same era.

E. Berti, V. Cardoso, and A. O. Starinets, Quasinormal modes of black holes and black branes, Class. Quant. Grav. 26

Original

2009

Cited alongside, same era.

D. Brizuela, J. M. Martin-Garcia, and M. Tiglio, A Complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole, Phys. Rev. D 80

Original

2009

Cited alongside, same era.

A. Dhani, Importance of mirror modes in binary black hole ringdown waveform, Phys. Rev. D 103

Original

2010

Cited alongside, same era.

Original

2016