Built on

Hugo von Zeipel, “Récherches sur le mouvement des petites planètes,” Ark. Astron. Mat. Fys. (1916), This reference is difficult to source. For a more recent exposition see, e.g., [ 71 ]
1916
Earlier work this paper cites.
Antoine Klein, Neil Cornish, and Nicolás Yunes, “Gravitational waveforms for precessing, quasicircular binaries via multiple scale analysis and uniform asymptotics: The near spin alignment case,” Phys. Rev. D88
Original
1932
Earlier work this paper cites.
Charles Darwin, “The gravity field of a particle,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 249
1959
Earlier work this paper cites.
D. Brouwer, “Solution of the problem of artificial satellite theory without drag,” Astronomical Journal 64
1959
Earlier work this paper cites.
Charles Darwin, “The gravity field of a particle. ii,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 263
1961
Earlier work this paper cites.
R. Ruffini and M. Sasaki, “On a Semirelativistic Treatment of the Gravitational Radiation From a Mass Thrusted Into a Black Hole,” Prog. Theor. Phys. 66
1981
Earlier work this paper cites.
Jirayr Kevorkian and Julian D Cole, Multiple scale and singular perturbation methods , Vol. 114 (Springer New York, 1996)
1996
Earlier work this paper cites.
Yasushi Mino, “Perturbative approach to an orbital evolution around a supermassive black hole,” Phys. Rev. D 67
2003
Earlier work this paper cites.
Leor Barack and Curt Cutler, “LISA capture sources: Approximate waveforms, signal-to-noise ratios, and parameter estimation accuracy,” Phys. Rev. D 69
2004
Earlier work this paper cites.
Thibault Damour, Achamveedu Gopakumar, and Bala R. Iyer, “Phasing of gravitational waves from inspiralling eccentric binaries,” Phys. Rev. D70
2004
Earlier work this paper cites.
Matteo Frigo and Steven G. Johnson, “The design and implementation of FFTW3,” Proceedings of the IEEE 93
2005
Earlier work this paper cites.
Steve Drasco and Scott A. Hughes, “Gravitational wave snapshots of generic extreme mass ratio inspirals,” Phys. Rev. D 73
2006
Earlier work this paper cites.
Jonathan R. Gair, Daniel J. Kennefick, and Shane L. Larson, “Semi-relativistic approximation to gravitational radiation from encounters with black holes,” Phys. Rev. D72
2006
Earlier work this paper cites.
Pranesh A. Sundararajan, Gaurav Khanna, and Scott A. Hughes, “Towards adiabatic waveforms for inspiral into Kerr black holes. I. A New model of the source for the time domain perturbation equation,” Phys. Rev. D76
2007
Earlier work this paper cites.
Tanja Hinderer and Eanna E. Flanagan, “Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion,” Phys. Rev. D D78
Original
2008
Earlier work this paper cites.
Stanislav Babak, Hua Fang, Jonathan R. Gair, Kostas Glampedakis, and Scott A. Hughes, “’Kludge’ gravitational waveforms for a test-body orbiting a Kerr black hole,” Phys. Rev. D75
2008
Earlier work this paper cites.
Yasushi Mino and Richard Price, “Two-timescale adiabatic expansion of a scalar field model,” Phys. Rev. D77
Original
2008
Earlier work this paper cites.
M. Galassi and B. Gough, GNU Scientific Library: Reference Manual , GNU manual (Network Theory, 2009)
2009
Earlier work this paper cites.
Leor Barack and Norichika Sago, “Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole,” Phys. Rev. D 81
Original
2010
Earlier work this paper cites.
Eric Poisson, Adam Pound, and Ian Vega, “The Motion of point particles in curved spacetime,” Living Rev. Rel. 14
Original
2011
Earlier work this paper cites.
E. A. Huerta and Jonathan R. Gair, “Influence of conservative corrections on parameter estimation for extreme-mass-ratio inspirals,” Phys. Rev. D79
Original
2011
Earlier work this paper cites.

Similar

E. A. Huerta and Jonathan R Gair, “Importance of including small body spin effects in the modelling of extreme and intermediate mass-ratio inspirals,” Phys. Rev. D84
Original
2011
Cited alongside, same era.
Frank Ohme, Mark Hannam, and Sascha Husa, “Reliability of complete gravitational waveform models for compact binary coalescences,” Phys. Rev. D84
Original
2011
Cited alongside, same era.
Peter Diener, Ian Vega, Barry Wardell, and Steven Detweiler, “Self-consistent orbital evolution of a particle around a Schwarzschild black hole,” Phys. Rev. Lett. 108
Original
2012
Cited alongside, same era.
Niels Warburton, Sarp Akcay, Leor Barack, Jonathan R. Gair, and Norichika Sago, “Evolution of inspiral orbits around a Schwarzschild black hole,” Phys. Rev. D 85
Original
2012
Cited alongside, same era.

Then

B. P. Abbott et al. (Virgo, LIGO Scientific), “Observation of Gravitational Waves from a Binary Black Hole Merger,” Phys. Rev. Lett. 116
Original
2016
Later among the works it cites.
Cesar Merlin, Amos Ori, Leor Barack, Adam Pound, and Maarten van de Meent, “Completion of metric reconstruction for a particle orbiting a Kerr black hole,” Phys. Rev. D 94
Original
2016
Later among the works it cites.
Maarten van de Meent, “Gravitational self-force on eccentric equatorial orbits around a Kerr black hole,” Phys. Rev. D 94
Original
2016
Later among the works it cites.
Thomas Osburn, Niels Warburton, and Charles R. Evans, “Highly eccentric inspirals into a black hole,” Phys. Rev. D93
Original
2016
Later among the works it cites.
Jeremy Miller, Barry Wardell, and Adam Pound, “Second-order perturbation theory: the problem of infinite mode coupling,” Phys. Rev. D 94

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2018

Fast Self-forced Inspirals

van de Meent, Maarten, Warburton, Niels

Understand

We present a new, fast method for computing the inspiral trajectory and gravitational waves from extreme mass-ratio inspirals that can incorporate all known (and future) self-force results.

Using near-identity (averaging) transformations we formulate equations of motion that do not explicitly depend upon the orbital phases of the inspiral, making them fast to evaluate, and whose solutions track the evolving constants of motion, orbital phases and waveform phase of a full self-force inspiral to $O(\eta)$, where $\eta$ is the (small) mass ratio.
As a concrete example, we implement these equations for inspirals of non-spinning (Schwarzschild) binaries.
Our code computes inspiral trajectories in milliseconds which is a speed up of 2-5 orders of magnitude (depending on the mass-ratio) over previous self-force inspiral models which take minutes to hours to evaluate.

Built on

Hugo von Zeipel, “Récherches sur le mouvement des petites planètes,” Ark. Astron. Mat. Fys. (1916), This reference is difficult to source. For a more recent exposition see, e.g., [ 71 ]
1916
Earlier work this paper cites.
Antoine Klein, Neil Cornish, and Nicolás Yunes, “Gravitational waveforms for precessing, quasicircular binaries via multiple scale analysis and uniform asymptotics: The near spin alignment case,” Phys. Rev. D88
Original
1932
Earlier work this paper cites.
Charles Darwin, “The gravity field of a particle,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 249
1959
Earlier work this paper cites.
D. Brouwer, “Solution of the problem of artificial satellite theory without drag,” Astronomical Journal 64
1959
Earlier work this paper cites.
Charles Darwin, “The gravity field of a particle. ii,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 263
1961
Earlier work this paper cites.
R. Ruffini and M. Sasaki, “On a Semirelativistic Treatment of the Gravitational Radiation From a Mass Thrusted Into a Black Hole,” Prog. Theor. Phys. 66
1981
Earlier work this paper cites.
Jirayr Kevorkian and Julian D Cole, Multiple scale and singular perturbation methods , Vol. 114 (Springer New York, 1996)
1996
Earlier work this paper cites.
Yasushi Mino, “Perturbative approach to an orbital evolution around a supermassive black hole,” Phys. Rev. D 67
2003
Earlier work this paper cites.
Leor Barack and Curt Cutler, “LISA capture sources: Approximate waveforms, signal-to-noise ratios, and parameter estimation accuracy,” Phys. Rev. D 69
2004
Earlier work this paper cites.
Thibault Damour, Achamveedu Gopakumar, and Bala R. Iyer, “Phasing of gravitational waves from inspiralling eccentric binaries,” Phys. Rev. D70
2004
Earlier work this paper cites.
Matteo Frigo and Steven G. Johnson, “The design and implementation of FFTW3,” Proceedings of the IEEE 93
2005
Earlier work this paper cites.
Steve Drasco and Scott A. Hughes, “Gravitational wave snapshots of generic extreme mass ratio inspirals,” Phys. Rev. D 73
2006
Earlier work this paper cites.
Jonathan R. Gair, Daniel J. Kennefick, and Shane L. Larson, “Semi-relativistic approximation to gravitational radiation from encounters with black holes,” Phys. Rev. D72
2006
Earlier work this paper cites.
Pranesh A. Sundararajan, Gaurav Khanna, and Scott A. Hughes, “Towards adiabatic waveforms for inspiral into Kerr black holes. I. A New model of the source for the time domain perturbation equation,” Phys. Rev. D76
2007
Earlier work this paper cites.
Tanja Hinderer and Eanna E. Flanagan, “Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion,” Phys. Rev. D D78
Original
2008
Earlier work this paper cites.
Stanislav Babak, Hua Fang, Jonathan R. Gair, Kostas Glampedakis, and Scott A. Hughes, “’Kludge’ gravitational waveforms for a test-body orbiting a Kerr black hole,” Phys. Rev. D75
2008
Earlier work this paper cites.
Yasushi Mino and Richard Price, “Two-timescale adiabatic expansion of a scalar field model,” Phys. Rev. D77
Original
2008
Earlier work this paper cites.
M. Galassi and B. Gough, GNU Scientific Library: Reference Manual , GNU manual (Network Theory, 2009)
2009
Earlier work this paper cites.
Leor Barack and Norichika Sago, “Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole,” Phys. Rev. D 81
Original
2010
Earlier work this paper cites.
Eric Poisson, Adam Pound, and Ian Vega, “The Motion of point particles in curved spacetime,” Living Rev. Rel. 14
Original
2011
Earlier work this paper cites.
E. A. Huerta and Jonathan R. Gair, “Influence of conservative corrections on parameter estimation for extreme-mass-ratio inspirals,” Phys. Rev. D79
Original
2011
Earlier work this paper cites.