Built on

Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, Phys. Rev. Lett. 122
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1901
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J. B. Gilmore and A. Ross, Phys. Rev. D 78
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B. S. Sathyaprakash, A. Buonanno, L. Lehner, C. Van Den Broeck, P. Ajith, A. Ghosh, K. Chatziioannou, P. Pani, M. Puerrer and S. Reddy, et al
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J. Droste. Proc. Acad. Sc i. Amst. 19:447–455 (1916); A. Einstein, L. Infeld and B. Hoffmann, Annals Math. 39
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Original
2001
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2001
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2002
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Then

Y. Kats, L. Motl and M. Padi, JHEP 12
2007
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2008
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G. Kälin, Z. Liu and R. A. Porto, [arXiv:2008.06047 [hep-th]]
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2020

Mining the Geodesic Equation for Scattering Data

Cheung, Clifford, Shah, Nabha, Solon, Mikhail P.

Understand

The geodesic equation encodes test-particle dynamics at arbitrary gravitational coupling, hence retaining all orders in the post-Minkowskian (PM) expansion.

Here we explore what geodesic motion can tell us about dynamical scattering in the presence of perturbatively small effects such as tidal distortion and higher derivative corrections to general relativity.
We derive an algebraic map between the perturbed geodesic equation and the leading PM scattering amplitude at arbitrary mass ratio.
As examples, we compute formulas for amplitudes and isotropic gauge Hamiltonians for certain infinite classes of tidal operators such as electric or magnetic Weyl to any power, and for higher derivative corrections to gravitationally interacting bodies with or without electric charge.

Built on

Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, Phys. Rev. Lett. 122
Original
1901
Earlier work this paper cites.
J. B. Gilmore and A. Ross, Phys. Rev. D 78
Original
1902
Earlier work this paper cites.
B. S. Sathyaprakash, A. Buonanno, L. Lehner, C. Van Den Broeck, P. Ajith, A. Ghosh, K. Chatziioannou, P. Pani, M. Puerrer and S. Reddy, et al
Original
1903
Earlier work this paper cites.
C. Cheung, J. Liu and G. N. Remmen, Phys. Rev. D 100
Original
1903
Earlier work this paper cites.
A. Brandhuber and G. Travaglini, JHEP 01
Original
1905
Earlier work this paper cites.
W. T. Emond and N. Moynihan, JHEP 12
Original
1905
Earlier work this paper cites.
A. Cristofoli, N. E. J. Bjerrum-Bohr, P. H. Damgaard and P. Vanhove, Phys. Rev. D 100
Original
1906
Earlier work this paper cites.
A. Cristofoli, Phys. Lett. B 800
Original
1906
Earlier work this paper cites.
S. Cai and K. D. Wang, [arXiv:1906.06850 [hep-th]]
Original
1906
Earlier work this paper cites.
Z. Bern, C. Cheung, R. Roiban, C. H. Shen, M. P. Solon and M. Zeng, JHEP 1910
Original
1908
Earlier work this paper cites.
H. Kawai, D. C. Lewellen and S. H. H. Tye, Nucl. Phys. B 269
Original
1909
Earlier work this paper cites.
N. Siemonsen and J. Vines, Phys. Rev. D 101
Original
1909
Earlier work this paper cites.
G. Kälin and R. A. Porto, JHEP 2001
Original
1910
Earlier work this paper cites.
N. E. J. Bjerrum-Bohr, A. Cristofoli and P. H. Damgaard, JHEP 08
Original
1910
Earlier work this paper cites.
G. Kälin and R. A. Porto, JHEP 2002
Original
1911
Earlier work this paper cites.
V. Vaidya, Phys. Rev. D 91
Original
1912
Earlier work this paper cites.
Q. Henry, G. Faye and L. Blanchet, Phys. Rev. D 101
Original
1912
Earlier work this paper cites.
N. Sennett, R. Brito, A. Buonanno, V. Gorbenko and L. Senatore, Phys. Rev. D 102
Original
1912
Earlier work this paper cites.
T. Damour, [arXiv:1912.02139 [gr-qc]]
Original
1912
Earlier work this paper cites.
E. E. Flanagan and T. Hinderer, Phys. Rev. D 77
Original
1915
Earlier work this paper cites.
B. Bertotti, Nuovo Cimento 4
1981
Earlier work this paper cites.
N. Wex and G. Schäfer, “Innermost stable orbits for coalescing binary systems of compact objects-a remark” Class. Quantum Grav. 10
1993
Earlier work this paper cites.
Y. Mino, M. Sasaki and T. Tanaka, Phys. Rev. D 55
1997
Earlier work this paper cites.

Similar

J. Droste. Proc. Acad. Sc i. Amst. 19:447–455 (1916); A. Einstein, L. Infeld and B. Hoffmann, Annals Math. 39
2000
Cited alongside, same era.
A. Buonanno and T. Damour, Phys. Rev. D 59
2000
Cited alongside, same era.
B. P. Abbott et al
Original
2001
Cited alongside, same era.
D. Bini, T. Damour and A. Geralico, Phys. Rev. D 101
Original
2001
Cited alongside, same era.
J. M. Henn and B. Mistlberger, JHEP 1905
Original
2002
Cited alongside, same era.
N. E. J. Bjerrum-Bohr, Phys. Rev. D 66