Built on

Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, “Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order,” Phys. Rev. Lett. 122
Original
1901
Earlier work this paper cites.
A. Antonelli, A. Buonanno, J. Steinhoff, M. van de Meent and J. Vines, “Energetics of two-body Hamiltonians in post-Minkowskian gravity,” Phys. Rev. D 99
Original
1901
Earlier work this paper cites.
S. Foffa and R. Sturani, “Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian,” Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
S. Foffa, R. A. Porto, I. Rothstein and R. Sturani, “Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian,” Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
S. Foffa and R. Sturani, “Hereditary Terms at Next-To-Leading Order in Two-Body Gravitational Dynamics,” arXiv:1907.02869 [gr-qc]
Original
1907
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C. Shen, M. P. Solon and M. Zeng, “Black Hole Binary Dynamics from the Double Copy and Effective Theory,” JHEP 10
Original
1908
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.
D. Bini, T. Damour and A. Geralico, “Novel approach to binary dynamics: application to the fifth post-Newtonian level,” Phys. Rev. Lett. 123
Original
1909
Earlier work this paper cites.
G. Kälin and R. A. Porto, “From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist),” JHEP 02
Original
1911
Earlier work this paper cites.
L. Blanchet, S. Foffa, F. Larrouturou and R. Sturani, “Logarithmic tail contributions to the energy function of circular compact binaries,” arXiv:1912.12359 [gr-qc]
Original
1912
Earlier work this paper cites.
T. Damour, “Classical and Quantum Scattering in Post-Minkowskian Gravity,” arXiv:1912.02139 [gr-qc]
Original
1912
Earlier work this paper cites.
J. A. Wheeler and R. P. Feynman, “Classical electrodynamics in terms of direct interparticle action,” Rev. Mod. Phys. 21
1949
Earlier work this paper cites.
L. Infeld, “Equations of Motion in General Relativity Theory and the Action Principle,” Rev. Mod. Phys. 29
1957
Earlier work this paper cites.
T. Damour and N. Deruelle, “Lagrangien généralisé du système de deux masses ponctuelles, à l’approximation post-post-newtonienne de la relativité générale,” C.R. Acad. Sc. Paris, Série II, 293
1981
Earlier work this paper cites.
T. Damour and N. Deruelle, “Radiation Reaction and Angular Momentum Loss in Small Angle Gravitational Scattering,” Phys. Lett. A 87
1981
Earlier work this paper cites.
T. Damour; “Problème des deux corps et freinage de rayonnement en relativité générale,” C.R. Acad. Sc. Paris, Série II, 294
1982
Earlier work this paper cites.
G. Schaefer, “The Gravitational Quadrupole Radiation Reaction Force and the Canonical Formalism of Adm,” Annals Phys. 161
1985
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. Roy. Soc. Lond. A 320
1986
Earlier work this paper cites.
L. Blanchet and T. Damour, “Tail Transported Temporal Correlations in the Dynamics of a Gravitating System,” Phys. Rev. D 37
1988
Earlier work this paper cites.
T. Damour and G. Schäfer, “Higher Order Relativistic Periastron Advances and Binary Pulsars,” Nuovo Cim. B 101
1988
Earlier work this paper cites.
L. Blanchet and T. Damour, “Post-newtonian Generation of Gravitational Waves,” Ann. Inst. H. Poincare Phys. Theor. 50
1989
Earlier work this paper cites.
T. Damour and B. R. Iyer, “PostNewtonian generation of gravitational waves. 2. The Spin moments,” Ann. Inst. H. Poincare Phys. Theor. 54
1991
Earlier work this paper cites.
T. Damour, M. Soffel and C. m. Xu, “General relativistic celestial mechanics. 1. Method and definition of reference systems,” Phys. Rev. D 43
1991
Earlier work this paper cites.

Similar

T. Damour and G. Schaefer, “Redefinition of position variables and the reduction of higher order Lagrangians,” J. Math. Phys. 32
1991
Cited alongside, same era.
T. Damour, M. Soffel and C. m. Xu, “General relativistic celestial mechanics. 2. Translational equations of motion,” Phys. Rev. D 45
1992
Cited alongside, same era.
G. Schäfer and N. Wex, “Second post-Newtonian motion of compact binaries,” Phys. Lett. A, 174
1993
Cited alongside, same era.
T. Damour and B. R. Iyer, “Generation of gravitational waves: The PostNewtonian spin octupole moment,” Class. Quant. Grav. 11
1995
Cited alongside, same era.
L. Blanchet, “Second postNewtonian generation of gravitational radiation,” Phys. Rev. D 51
1995
Cited alongside, same era.

Then

A. Ross, “Multipole expansion at the level of the action,” Phys. Rev. D 85
Original
2012
Later among the works it cites.
A. Le Tiec, L. Blanchet and B. F. Whiting, “The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory,” Phys. Rev. D 85
Original
2012
Later among the works it cites.
E. Barausse, A. Buonanno and A. Le Tiec, “The complete non-spinning effective-one-body metric at linear order in the mass ratio,” Phys. Rev. D 85
Original
2012
Later among the works it cites.
S. Foffa and R. Sturani, “Tail terms in gravitational radiation reaction via effective field theory,” Phys. Rev. D 87
Original
2013
Later among the works it cites.
D. Bini and T. Damour, “Analytical determination of the two-body gravitational interaction potential at the fourth post-Newtonian approximation,” Phys. Rev. D 87

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2020

Sixth post-Newtonian local-in-time dynamics of binary systems

Bini, Donato, Damour, Thibault, Geralico, Andrea

Understand

Using a recently introduced method [Phys.\ Rev.\ Lett.\ {\bf 123}, 231104 (2019)], which splits the conservative dynamics of gravitationally interacting binary systems into a non-local-in-time part and a local-in-time one, we compute the local part of the dynamics at the sixth post-Newtonian (6PN) accuracy.

Our strategy combines several theoretical formalisms: post-Newtonian, post-Minkowskian, multipolar-post-Minkowskian, effective-field-theory, gravitational self-force, effective one-body, and Delaunay averaging.
The full functional structure of the local 6PN Hamiltonian (which involves 151 numerical coefficients) is derived, but contains four undetermined numerical coefficients.
Our 6PN-accurate results are complete at orders $G^3$ and $G^4$, and the derived $O(G^3)$ scattering angle agrees, within our 6PN accuracy, with the computation of [Phys.\ Rev.\ Lett.\ {\bf 122}, no.

Built on

Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, “Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order,” Phys. Rev. Lett. 122
Original
1901
Earlier work this paper cites.
A. Antonelli, A. Buonanno, J. Steinhoff, M. van de Meent and J. Vines, “Energetics of two-body Hamiltonians in post-Minkowskian gravity,” Phys. Rev. D 99
Original
1901
Earlier work this paper cites.
S. Foffa and R. Sturani, “Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian,” Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
S. Foffa, R. A. Porto, I. Rothstein and R. Sturani, “Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian,” Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
S. Foffa and R. Sturani, “Hereditary Terms at Next-To-Leading Order in Two-Body Gravitational Dynamics,” arXiv:1907.02869 [gr-qc]
Original
1907
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C. Shen, M. P. Solon and M. Zeng, “Black Hole Binary Dynamics from the Double Copy and Effective Theory,” JHEP 10
Original
1908
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.
D. Bini, T. Damour and A. Geralico, “Novel approach to binary dynamics: application to the fifth post-Newtonian level,” Phys. Rev. Lett. 123
Original
1909
Earlier work this paper cites.
G. Kälin and R. A. Porto, “From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist),” JHEP 02
Original
1911
Earlier work this paper cites.
L. Blanchet, S. Foffa, F. Larrouturou and R. Sturani, “Logarithmic tail contributions to the energy function of circular compact binaries,” arXiv:1912.12359 [gr-qc]
Original
1912
Earlier work this paper cites.
T. Damour, “Classical and Quantum Scattering in Post-Minkowskian Gravity,” arXiv:1912.02139 [gr-qc]
Original
1912
Earlier work this paper cites.
J. A. Wheeler and R. P. Feynman, “Classical electrodynamics in terms of direct interparticle action,” Rev. Mod. Phys. 21
1949
Earlier work this paper cites.
L. Infeld, “Equations of Motion in General Relativity Theory and the Action Principle,” Rev. Mod. Phys. 29
1957
Earlier work this paper cites.
T. Damour and N. Deruelle, “Lagrangien généralisé du système de deux masses ponctuelles, à l’approximation post-post-newtonienne de la relativité générale,” C.R. Acad. Sc. Paris, Série II, 293
1981
Earlier work this paper cites.
T. Damour and N. Deruelle, “Radiation Reaction and Angular Momentum Loss in Small Angle Gravitational Scattering,” Phys. Lett. A 87
1981
Earlier work this paper cites.
T. Damour; “Problème des deux corps et freinage de rayonnement en relativité générale,” C.R. Acad. Sc. Paris, Série II, 294
1982
Earlier work this paper cites.
G. Schaefer, “The Gravitational Quadrupole Radiation Reaction Force and the Canonical Formalism of Adm,” Annals Phys. 161
1985
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. Roy. Soc. Lond. A 320
1986
Earlier work this paper cites.
L. Blanchet and T. Damour, “Tail Transported Temporal Correlations in the Dynamics of a Gravitating System,” Phys. Rev. D 37
1988
Earlier work this paper cites.
T. Damour and G. Schäfer, “Higher Order Relativistic Periastron Advances and Binary Pulsars,” Nuovo Cim. B 101
1988
Earlier work this paper cites.
L. Blanchet and T. Damour, “Post-newtonian Generation of Gravitational Waves,” Ann. Inst. H. Poincare Phys. Theor. 50
1989
Earlier work this paper cites.
T. Damour and B. R. Iyer, “PostNewtonian generation of gravitational waves. 2. The Spin moments,” Ann. Inst. H. Poincare Phys. Theor. 54
1991
Earlier work this paper cites.
T. Damour, M. Soffel and C. m. Xu, “General relativistic celestial mechanics. 1. Method and definition of reference systems,” Phys. Rev. D 43
1991
Earlier work this paper cites.

Similar

T. Damour and G. Schaefer, “Redefinition of position variables and the reduction of higher order Lagrangians,” J. Math. Phys. 32
1991
Cited alongside, same era.
T. Damour, M. Soffel and C. m. Xu, “General relativistic celestial mechanics. 2. Translational equations of motion,” Phys. Rev. D 45
1992
Cited alongside, same era.
G. Schäfer and N. Wex, “Second post-Newtonian motion of compact binaries,” Phys. Lett. A, 174
1993
Cited alongside, same era.
T. Damour and B. R. Iyer, “Generation of gravitational waves: The PostNewtonian spin octupole moment,” Class. Quant. Grav. 11
1995
Cited alongside, same era.
L. Blanchet, “Second postNewtonian generation of gravitational radiation,” Phys. Rev. D 51
1995
Cited alongside, same era.

Then

A. Ross, “Multipole expansion at the level of the action,” Phys. Rev. D 85
Original
2012
Later among the works it cites.
A. Le Tiec, L. Blanchet and B. F. Whiting, “The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory,” Phys. Rev. D 85
Original
2012
Later among the works it cites.
E. Barausse, A. Buonanno and A. Le Tiec, “The complete non-spinning effective-one-body metric at linear order in the mass ratio,” Phys. Rev. D 85
Original
2012
Later among the works it cites.
S. Foffa and R. Sturani, “Tail terms in gravitational radiation reaction via effective field theory,” Phys. Rev. D 87
Original
2013
Later among the works it cites.
D. Bini and T. Damour, “Analytical determination of the two-body gravitational interaction potential at the fourth post-Newtonian approximation,” Phys. Rev. D 87

Beyond the bibliography

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

Open on alphaXiv

alphaXiv is searching for related work…

T. Damour and G. Esposito-Farese, “Testing gravity to second postNewtonian order: A Field theory approach,” Phys. Rev. D 53

1996

Cited alongside, same era.

L. Blanchet, T. Damour and B. R. Iyer, “Gravitational waves from inspiralling compact binaries: Energy loss and wave form to second postNewtonian order,” Phys. Rev. D 51

1996

Cited alongside, same era.

L. Blanchet, “On the multipole expansion of the gravitational field,” Class. Quant. Grav. 15

1998

Cited alongside, same era.

T. Damour, P. Jaranowski, and G. Schäfer, “On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation,” Phys. Rev. D 62

2000

Cited alongside, same era.

O. Poujade and L. Blanchet, “Post-Newtonian approximation for isolated systems calculated by matched asymptotic expansions,” Phys. Rev. D 65

2002

Cited alongside, same era.

D. Bini, T. Damour and A. Geralico, “Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders,” arXiv:2003.11891 [gr-qc]