Built on

A. Antonelli, M. van de Meent, A. Buonanno, J. Steinhoff, and J. Vines, Quasicircular inspirals and plunges from nonspinning effective-one-body Hamiltonians with gravitational self-force information, Phys. Rev. D 101
Original
1907
Earlier work this paper cites.
A. Pound, B. Wardell, N. Warburton, and J. Miller, Second-order self-force calculation of gravitational binding energy in compact binaries, Phys. Rev. Lett. 124
Original
1908
Earlier work this paper cites.
N. E. M. Rifat, S. E. Field, G. Khanna, and V. Varma, Surrogate model for gravitational wave signals from comparable and large-mass-ratio black hole binaries, Phys. Rev. D 101
Original
1910
Earlier work this paper cites.
T. Damour, Classical and quantum scattering in post-Minkowskian gravity, Phys. Rev. D 102
Original
1912
Earlier work this paper cites.
M. Mathisson, Neue mechanik materieller systemes, Acta Phys. Polon. 6
1937
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. Geroch, Multipole moments. II. Curved space, J. Math. Phys. 11
1970
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.
R. O. Hansen, Multipole moments of stationary space-times, J. Math. Phys. 15
1974
Earlier work this paper cites.
P. D. D’Eath, Dynamics of a small black hole in a background universe, Phys. Rev. D 11
1975
Earlier work this paper cites.
P. L. Chrzanowski, Vector potential and metric perturbations of a rotating black hole, Phys. Rev. D 11
1975
Earlier work this paper cites.
R. M. Wald, Construction of solutions of gravitational, electromagnetic, or other perturbation equations from solutions of decoupled equations, Phys. Rev. Lett. 41
1978
Earlier work this paper cites.
W. Eckhaus, Asymptotic Analysis of Singular Perturbations , Studies in Mathematics and Its Applications, Vol. 9 (Elsevier North-Holland, New York, 1979)
1979
Earlier work this paper cites.
L. Blanchet and T. Damour, Radiative gravitational fields in general relativity I. General structure of the field outside the source, Phil. Trans. R. Soc. Lond. A 320
1986
Earlier work this paper cites.
J. I. Richards and H. K. Youn, The Theory of Distributions: A Nontechnical Introduction (Cambridge University Press, 1990)
1990
Earlier work this paper cites.
J. Kevorkian and J. D. Cole, Multiple Scale and Singular Perturbation Methods , Applied Mathematical Sciences, Vol. 114 (Springer New York, 1996)
1996
Earlier work this paper cites.
M. Bruni, S. Matarrese, S. Mollerach, and S. Sonego, Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond, Class. Quant. Grav. 14
1997
Earlier work this paper cites.
S. Detweiler and B. F. Whiting, Self-force via a Green’s function decomposition, Phys. Rev. D 67
2003
Earlier work this paper cites.
R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), GW190412: Observation of a binary-black-hole coalescence with asymmetric masses, Phys. Rev. D 102
Original
2004
Earlier work this paper cites.
L. Barack and C. O. Lousto, Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation, Phys. Rev. D 72
2005
Earlier work this paper cites.
E. Poisson, Metric of a tidally distorted nonrotating black hole, Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
J. Miller and A. Pound, Two-timescale evolution of extreme-mass-ratio inspirals: Waveform generation scheme for quasicircular orbits in Schwarzschild spacetime, Phys. Rev. D 103
Original
2006
Earlier work this paper cites.
M. van de Meent and H. P. Pfeiffer, Intermediate mass-ratio black hole binaries: Applicability of small mass-ratio perturbation theory, Phys. Rev. Lett. 125
Original
2006
Earlier work this paper cites.
R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), GW190814: Gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object, Astrophys. J. Lett. 896
Original
2006
Earlier work this paper cites.
E. Rosenthal, Construction of the second-order gravitational perturbations produced by a compact object, Phys. Rev. D 73
2006
Earlier work this paper cites.
L. Barack and D. A. Golbourn, Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in 2 + 1 2+1 dimensions, Phys. Rev. D 76
Original
2007
Earlier work this paper cites.

Similar

T. Hinderer and É. É. Flanagan, Two-timescale analysis of extreme mass ratio inspirals in Kerr spacetime: Orbital motion, Phys. Rev. D 78
Original
2008
Cited alongside, same era.
R. Fujita and M. Shibata, Extreme mass ratio inspirals on the equatorial plane in the adiabatic order, Phys. Rev. D 102
Original
2008
Cited alongside, same era.
S. E. Gralla and R. M. Wald, A rigorous derivation of gravitational self-force, Class. Quant. Grav. 25
Original
2008
Cited alongside, same era.
I. Vega and S. Detweiler, Regularization of fields for self-force problems in curved spacetime: Foundations and a time-domain application, Phys. Rev. D 77
Original
2008
Cited alongside, same era.
J. M. Martín-García, xPerm: fast index canonicalization for tensor computer algebra, Comp. Phys. Commun. 179

Then

A. Pound, Motion of small objects in curved spacetimes: An introduction to gravitational self-force, in Equations of Motion in Relativistic Gravity , Fundamental Theories of Physics, Vol. 179, edited by D. Pützfeld, C. Lämmerzahl, and B. Schutz (Springer, 2015) pp. 399–486, arXiv:1506.06245 [gr-qc]
Original
2015
Later among the works it cites.
B. Wardell, Self-force: Computational strategies, in Equations of Motion in Relativistic Gravity , Fundamental Theories of Physics, Vol. 179, edited by D. Pützfeld, C. Lämmerzahl, and B. Schutz (Springer, 2015) pp. 487–522, arXiv:1501.07322 [gr-qc]
Original
2015
Later among the works it cites.
B. Wardell and N. Warburton, Applying the effective-source approach to frequency-domain self-force calculations: Lorenz-gauge gravitational perturbations, Phys. Rev. D 92
Original
2015
Later among the works it cites.
T. Osburn, N. Warburton, and C. R. Evans, Highly eccentric inspirals into a black hole, Phys. Rev. D 93
Original
2016
Later among the works it cites.

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

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2021

Second-order gravitational self-force in a highly regular gauge

Upton, Samuel D., Pound, Adam

Understand

Extreme-mass-ratio inspirals (EMRIs) will be key sources for LISA.

However, accurately extracting system parameters from a detected EMRI waveform will require self-force calculations at second order in perturbation theory, which are still in a nascent stage.
One major obstacle in these calculations is the strong divergences that are encountered on the worldline of the small object.
Previously, it was shown by one of us [Phys.

Built on

A. Antonelli, M. van de Meent, A. Buonanno, J. Steinhoff, and J. Vines, Quasicircular inspirals and plunges from nonspinning effective-one-body Hamiltonians with gravitational self-force information, Phys. Rev. D 101
Original
1907
Earlier work this paper cites.
A. Pound, B. Wardell, N. Warburton, and J. Miller, Second-order self-force calculation of gravitational binding energy in compact binaries, Phys. Rev. Lett. 124
Original
1908
Earlier work this paper cites.
N. E. M. Rifat, S. E. Field, G. Khanna, and V. Varma, Surrogate model for gravitational wave signals from comparable and large-mass-ratio black hole binaries, Phys. Rev. D 101
Original
1910
Earlier work this paper cites.
T. Damour, Classical and quantum scattering in post-Minkowskian gravity, Phys. Rev. D 102
Original
1912
Earlier work this paper cites.
M. Mathisson, Neue mechanik materieller systemes, Acta Phys. Polon. 6
1937
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. Geroch, Multipole moments. II. Curved space, J. Math. Phys. 11
1970
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.
R. O. Hansen, Multipole moments of stationary space-times, J. Math. Phys. 15
1974
Earlier work this paper cites.
P. D. D’Eath, Dynamics of a small black hole in a background universe, Phys. Rev. D 11
1975
Earlier work this paper cites.
P. L. Chrzanowski, Vector potential and metric perturbations of a rotating black hole, Phys. Rev. D 11
1975
Earlier work this paper cites.
R. M. Wald, Construction of solutions of gravitational, electromagnetic, or other perturbation equations from solutions of decoupled equations, Phys. Rev. Lett. 41
1978
Earlier work this paper cites.
W. Eckhaus, Asymptotic Analysis of Singular Perturbations , Studies in Mathematics and Its Applications, Vol. 9 (Elsevier North-Holland, New York, 1979)
1979
Earlier work this paper cites.
L. Blanchet and T. Damour, Radiative gravitational fields in general relativity I. General structure of the field outside the source, Phil. Trans. R. Soc. Lond. A 320
1986
Earlier work this paper cites.
J. I. Richards and H. K. Youn, The Theory of Distributions: A Nontechnical Introduction (Cambridge University Press, 1990)
1990
Earlier work this paper cites.
J. Kevorkian and J. D. Cole, Multiple Scale and Singular Perturbation Methods , Applied Mathematical Sciences, Vol. 114 (Springer New York, 1996)
1996
Earlier work this paper cites.
M. Bruni, S. Matarrese, S. Mollerach, and S. Sonego, Perturbations of spacetime: gauge transformations and gauge invariance at second order and beyond, Class. Quant. Grav. 14
1997
Earlier work this paper cites.
S. Detweiler and B. F. Whiting, Self-force via a Green’s function decomposition, Phys. Rev. D 67
2003
Earlier work this paper cites.
R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), GW190412: Observation of a binary-black-hole coalescence with asymmetric masses, Phys. Rev. D 102
Original
2004
Earlier work this paper cites.
L. Barack and C. O. Lousto, Perturbations of Schwarzschild black holes in the Lorenz gauge: Formulation and numerical implementation, Phys. Rev. D 72
2005
Earlier work this paper cites.
E. Poisson, Metric of a tidally distorted nonrotating black hole, Phys. Rev. Lett. 94
2005
Earlier work this paper cites.
J. Miller and A. Pound, Two-timescale evolution of extreme-mass-ratio inspirals: Waveform generation scheme for quasicircular orbits in Schwarzschild spacetime, Phys. Rev. D 103
Original
2006
Earlier work this paper cites.
M. van de Meent and H. P. Pfeiffer, Intermediate mass-ratio black hole binaries: Applicability of small mass-ratio perturbation theory, Phys. Rev. Lett. 125
Original
2006
Earlier work this paper cites.
R. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration), GW190814: Gravitational waves from the coalescence of a 23 solar mass black hole with a 2.6 solar mass compact object, Astrophys. J. Lett. 896
Original
2006
Earlier work this paper cites.
E. Rosenthal, Construction of the second-order gravitational perturbations produced by a compact object, Phys. Rev. D 73
2006
Earlier work this paper cites.
L. Barack and D. A. Golbourn, Scalar-field perturbations from a particle orbiting a black hole using numerical evolution in 2 + 1 2+1 dimensions, Phys. Rev. D 76
Original
2007
Earlier work this paper cites.

Similar

T. Hinderer and É. É. Flanagan, Two-timescale analysis of extreme mass ratio inspirals in Kerr spacetime: Orbital motion, Phys. Rev. D 78
Original
2008
Cited alongside, same era.
R. Fujita and M. Shibata, Extreme mass ratio inspirals on the equatorial plane in the adiabatic order, Phys. Rev. D 102
Original
2008
Cited alongside, same era.
S. E. Gralla and R. M. Wald, A rigorous derivation of gravitational self-force, Class. Quant. Grav. 25
Original
2008
Cited alongside, same era.
I. Vega and S. Detweiler, Regularization of fields for self-force problems in curved spacetime: Foundations and a time-domain application, Phys. Rev. D 77
Original
2008
Cited alongside, same era.
J. M. Martín-García, xPerm: fast index canonicalization for tensor computer algebra, Comp. Phys. Commun. 179

Then

A. Pound, Motion of small objects in curved spacetimes: An introduction to gravitational self-force, in Equations of Motion in Relativistic Gravity , Fundamental Theories of Physics, Vol. 179, edited by D. Pützfeld, C. Lämmerzahl, and B. Schutz (Springer, 2015) pp. 399–486, arXiv:1506.06245 [gr-qc]
Original
2015
Later among the works it cites.
B. Wardell, Self-force: Computational strategies, in Equations of Motion in Relativistic Gravity , Fundamental Theories of Physics, Vol. 179, edited by D. Pützfeld, C. Lämmerzahl, and B. Schutz (Springer, 2015) pp. 487–522, arXiv:1501.07322 [gr-qc]
Original
2015
Later among the works it cites.
B. Wardell and N. Warburton, Applying the effective-source approach to frequency-domain self-force calculations: Lorenz-gauge gravitational perturbations, Phys. Rev. D 92
Original
2015
Later among the works it cites.
T. Osburn, N. Warburton, and C. R. Evans, Highly eccentric inspirals into a black hole, Phys. Rev. D 93
Original
2016
Later among the works it cites.

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

2008

Cited alongside, same era.

L. Barack, Gravitational self force in extreme mass-ratio inspirals, Class. Quant. Grav. 26

Original

2009

Cited alongside, same era.

D. Brizuela, J. M. Martín-García, and G. A. M. Marugán, xPert: Computer algebra for metric perturbation theory, Gen. Rel. Grav. 41

Original

2009

Cited alongside, same era.

T. Damour, Gravitational self-force in a Schwarzschild background and the effective one-body formalism, Phys. Rev. D 81

Original

2010

Cited alongside, same era.

L. Barack, T. Damour, and N. Sago, Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism, Phys. Rev. D 82

Original

2010

Cited alongside, same era.

A. Pound, Self-consistent gravitational self-force, Phys. Rev. D 81

Original

2010

Cited alongside, same era.

E. Poisson and I. Vlasov, Geometry and dynamics of a tidally deformed black hole, Phys. Rev. D 81

Original

2010

Cited alongside, same era.

E. Poisson, A. Pound, and I. Vega, The motion of point particles in curved spacetime, Living Rev. Relativ. 14

Original

2011

Cited alongside, same era.

J. Miller, B. Wardell, and A. Pound, Second-order perturbation theory: The problem of infinite mode coupling, Phys. Rev. D 94

Original

2016