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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.
A. Koemans Collado, P. Di Vecchia and R. Russo, “Revisiting the 2PM eikonal and the dynamics of binary black holes,” Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
A. Brandhuber and G. Travaglini, “On higher-derivative effects on the gravitational potential and particle bending,” arXiv:1905.05657 [hep-th]
Original
1905
Earlier work this paper cites.
W. T. Emond and N. Moynihan, “Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity,” arXiv:1905.08213 [hep-th]
Original
1905
Earlier work this paper cites.
A. Cristofoli, N. E. J. Bjerrum-Bohr, P. H. Damgaard and P. Vanhove, “On Post-Minkowskian Hamiltonians in General Relativity,” arXiv:1906.01579 [hep-th]
Original
1906
Earlier work this paper cites.
B. Maybee, D. O’Connell and J. Vines, “Observables and amplitudes for spinning particles and black holes,” arXiv:1906.09260 [hep-th]
Original
1906
Earlier work this paper cites.
A. Guevara, A. Ochirov and J. Vines, “Black-hole scattering with general spin directions from minimal-coupling amplitudes,” arXiv:1906.10071 [hep-th]
Original
1906
Earlier work this paper cites.
N. Arkani-Hamed, Y. t. Huang and D. O’Connell, “Kerr Black Holes as Elementary Particles,” arXiv:1906.10100 [hep-th]
Original
1906
Earlier work this paper cites.
A. Cristofoli, “Post-Minkowskian Hamiltonians in Modified Theories of Gravity,” arXiv:1906.05209 [hep-th]
Original
1906
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, “Black Hole Binary Dynamics from the Double Copy and Effective Theory,” arXiv:1908.01493 [hep-th]
Original
1908
Earlier work this paper cites.

Similar

P. H. Damgaard, K. Haddad and A. Helset, “Heavy Black Hole Effective Theory,” arXiv:1908.10308 [hep-ph]
Original
1908
Cited alongside, same era.
G. Kälin and R. A. Porto, “From Boundary Data to Bound States,” arXiv:1910.03008 [hep-th]
Original
1910
Cited alongside, same era.
R. L. Sugar and R. Blankenbecler, “Eikonal expansion,” Phys. Rev. 183
1969
Cited alongside, same era.
S. J. Wallace, “Eikonal expansion,” Annals Phys. 78
1973
Cited alongside, same era.
A. Paliov and S. Rosendorff, “Exponentially small scattering amplitude in high energy potential scattering. 2.,” J. Math. Phys. 15
1974
Cited alongside, same era.
G. ’t Hooft, Phys. Lett. B 198

Then

N. E. J. Bjerrum-Bohr, J. F. Donoghue, B. R. Holstein, L. Planté and P. Vanhove, “Light-like Scattering in Quantum Gravity,” JHEP 1611
Original
2016
Later among the works it cites.
T. Damour, “High-energy gravitational scattering and the general relativistic two-body problem,” Phys. Rev. D 97
Original
2018
Later among the works it cites.
N. E. J. Bjerrum-Bohr, P. H. Damgaard, G. Festuccia, L. Planté and P. Vanhove, “General Relativity from Scattering Amplitudes,” Phys. Rev. Lett. 121
Original
2018
Later among the works it cites.
C. Cheung, I. Z. Rothstein and M. P. Solon, “From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion,” Phys. Rev. Lett. 121
Original
2018
Later among the works it cites.
J. Vines, “Scattering of two spinning black holes in post-Minkowskian gravity, to all orders in spin, and effective-one-body mappings,” Class. Quant. Grav. 35

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2019

Post-Minkowskian Scattering Angle in Einstein Gravity

Bjerrum-Bohr, N. E. J., Cristofoli, Andrea, Damgaard, Poul H.

Understand

Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system.

A corollary is that the scattering angle can be computed from the amplitude itself, without having to introduce a potential.
All results are universal and provide for the case of general relativity a very simple formula for the scattering angle in terms of the classical part of the amplitude, to any order in the post-Minkowskian expansion.

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.
A. Koemans Collado, P. Di Vecchia and R. Russo, “Revisiting the 2PM eikonal and the dynamics of binary black holes,” Phys. Rev. D 100
Original
1904
Earlier work this paper cites.
A. Brandhuber and G. Travaglini, “On higher-derivative effects on the gravitational potential and particle bending,” arXiv:1905.05657 [hep-th]
Original
1905
Earlier work this paper cites.
W. T. Emond and N. Moynihan, “Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity,” arXiv:1905.08213 [hep-th]
Original
1905
Earlier work this paper cites.
A. Cristofoli, N. E. J. Bjerrum-Bohr, P. H. Damgaard and P. Vanhove, “On Post-Minkowskian Hamiltonians in General Relativity,” arXiv:1906.01579 [hep-th]
Original
1906
Earlier work this paper cites.
B. Maybee, D. O’Connell and J. Vines, “Observables and amplitudes for spinning particles and black holes,” arXiv:1906.09260 [hep-th]
Original
1906
Earlier work this paper cites.
A. Guevara, A. Ochirov and J. Vines, “Black-hole scattering with general spin directions from minimal-coupling amplitudes,” arXiv:1906.10071 [hep-th]
Original
1906
Earlier work this paper cites.
N. Arkani-Hamed, Y. t. Huang and D. O’Connell, “Kerr Black Holes as Elementary Particles,” arXiv:1906.10100 [hep-th]
Original
1906
Earlier work this paper cites.
A. Cristofoli, “Post-Minkowskian Hamiltonians in Modified Theories of Gravity,” arXiv:1906.05209 [hep-th]
Original
1906
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, “Black Hole Binary Dynamics from the Double Copy and Effective Theory,” arXiv:1908.01493 [hep-th]
Original
1908
Earlier work this paper cites.

Similar

P. H. Damgaard, K. Haddad and A. Helset, “Heavy Black Hole Effective Theory,” arXiv:1908.10308 [hep-ph]
Original
1908
Cited alongside, same era.
G. Kälin and R. A. Porto, “From Boundary Data to Bound States,” arXiv:1910.03008 [hep-th]
Original
1910
Cited alongside, same era.
R. L. Sugar and R. Blankenbecler, “Eikonal expansion,” Phys. Rev. 183
1969
Cited alongside, same era.
S. J. Wallace, “Eikonal expansion,” Annals Phys. 78
1973
Cited alongside, same era.
A. Paliov and S. Rosendorff, “Exponentially small scattering amplitude in high energy potential scattering. 2.,” J. Math. Phys. 15
1974
Cited alongside, same era.
G. ’t Hooft, Phys. Lett. B 198