Abstract
We employ the “KMOC” formalism of [1] to compute classical momentum deflections of spinning bodies with arbitrary spin orientations up to next-to-leading order (one loop). We do this in electrodynamics and gravity. The final result, valid for generic masses, is true for all spins at tree level and up to second (fourth) spin order for the electromagnetic (gravity) case at one loop. Furthermore, emphasis is given to the probe limit scenario where our results extend to all spin orders in the heavy source, even at next-to-leading order. We carry out our computations both using a unitarity based framework and Feynman diagrammatic approach which relies on scattering amplitudes computed on fixed backgrounds.
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D.A. Kosower, B. Maybee and D. O’Connell, Amplitudes, Observables, and Classical Scattering, JHEP 02 (2019) 137 [arXiv:1811.10950] [INSPIRE].
LIGO Scientific and Virgo collaborations, Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116 (2016) 061102 [arXiv:1602.03837] [INSPIRE].
LIGO Scientific and Virgo collaborations, GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence, Phys. Rev. Lett. 116 (2016) 241103 [arXiv:1606.04855] [INSPIRE].
LIGO Scientific and VIRGO collaborations, GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2, Phys. Rev. Lett. 118 (2017) 221101 [Erratum ibid. 121 (2018) 129901] [arXiv:1706.01812] [INSPIRE].
LIGO Scientific and Virgo collaborations, GW170814: A Three-Detector Observation of Gravitational Waves from a Binary Black Hole Coalescence, Phys. Rev. Lett. 119 (2017) 141101 [arXiv:1709.09660] [INSPIRE].
LIGO Scientific and Virgo collaborations, GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral, Phys. Rev. Lett. 119 (2017) 161101 [arXiv:1710.05832] [INSPIRE].
A. Buonanno and T. Damour, Effective one-body approach to general relativistic two-body dynamics, Phys. Rev. D 59 (1999) 084006 [gr-qc/9811091] [INSPIRE].
A. Buonanno and T. Damour, Transition from inspiral to plunge in binary black hole coalescences, Phys. Rev. D 62 (2000) 064015 [gr-qc/0001013] [INSPIRE].
T. Damour, Coalescence of two spinning black holes: an effective one-body approach, Phys. Rev. D 64 (2001) 124013 [gr-qc/0103018] [INSPIRE].
T. Damour, P. Jaranowski and G. Schaefer, On the determination of the last stable orbit for circular general relativistic binaries at the third postNewtonian approximation, Phys. Rev. D 62 (2000) 084011 [gr-qc/0005034] [INSPIRE].
F. Pretorius, Evolution of binary black hole spacetimes, Phys. Rev. Lett. 95 (2005) 121101 [gr-qc/0507014] [INSPIRE].
W.D. Goldberger and I.Z. Rothstein, An Effective field theory of gravity for extended objects, Phys. Rev. D 73 (2006) 104029 [hep-th/0409156] [INSPIRE].
R.A. Porto, The effective field theorist’s approach to gravitational dynamics, Phys. Rept. 633 (2016) 1 [arXiv:1601.04914] [INSPIRE].
D. Neill and I.Z. Rothstein, Classical Space-Times from the S Matrix, Nucl. Phys. B 877 (2013) 177 [arXiv:1304.7263] [INSPIRE].
N.E.J. Bjerrum-Bohr, J.F. Donoghue and P. Vanhove, On-shell Techniques and Universal Results in Quantum Gravity, JHEP 02 (2014) 111 [arXiv:1309.0804] [INSPIRE].
N.E.J. Bjerrum-Bohr, B.R. Holstein, L. Planté and P. Vanhove, Graviton-Photon Scattering, Phys. Rev. D 91 (2015) 064008 [arXiv:1410.4148] [INSPIRE].
N.E.J. Bjerrum-Bohr, J.F. Donoghue, B.R. Holstein, L. Planté and P. Vanhove, Bending of Light in Quantum Gravity, Phys. Rev. Lett. 114 (2015) 061301 [arXiv:1410.7590] [INSPIRE].
N.E.J. Bjerrum-Bohr, J.F. Donoghue, B.R. Holstein, L. Plante and P. Vanhove, Light-like Scattering in Quantum Gravity, JHEP 11 (2016) 117 [arXiv:1609.07477] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, G. Festuccia, L. Planté and P. Vanhove, General Relativity from Scattering Amplitudes, Phys. Rev. Lett. 121 (2018) 171601 [arXiv:1806.04920] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, L. Planté and P. Vanhove, Classical gravity from loop amplitudes, Phys. Rev. D 104 (2021) 026009 [arXiv:2104.04510] [INSPIRE].
N.E.J. Bjerrum-Bohr, P.H. Damgaard, L. Planté and P. Vanhove, The amplitude for classical gravitational scattering at third Post-Minkowskian order, JHEP 08 (2021) 172 [arXiv:2105.05218] [INSPIRE].
E. Herrmann, J. Parra-Martinez, M.S. Ruf and M. Zeng, Radiative classical gravitational observables at \( \mathcal{O} \)(G3) from scattering amplitudes, JHEP 10 (2021) 148 [arXiv:2104.03957] [INSPIRE].
A. Cristofoli, R. Gonzo, D.A. Kosower and D. O’Connell, Waveforme] [INSPIRE].
Z. Bern, A. Luna, R. Roiban, C.-H. Shen and M. Zeng, Spinning black hole binary dynamics, scattering amplitudes, and effective field theory, Phys. Rev. D 104 (2021) 065014 [arXiv:2005.03071] [INSPIRE].
Z. Bern, J. Parra-Martinez, R. Roiban, M.S. Ruf, C.-H. Shen, M.P. Solon et al., Scattering Amplitudes and Conservative Binary Dynamics at \( \mathcal{O} \)(G4), Phys. Rev. Lett. 126 (2021) 171601 [arXiv:2101.07254] [INSPIRE].
E. Herrmann, J. Parra-Martinez, M.S. Ruf and M. Zeng, Gravitational Bremsstrahlung from Reverse Unitarity, Phys. Rev. Lett. 126 (2021) 201602 [arXiv:2101.07255] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, The eikonal approach to gravitational scattering and radiation at \( \mathcal{O} \)(G3), JHEP 07 (2021) 169 [arXiv:2104.03256] [INSPIRE].
Y.F. Bautista, A. Guevara, C. Kavanagh and J. Vines, From Scattering in Black Hole Backgrounds to Higher-Spin Amplitudes: Part I, arXiv:2107.10179 [INSPIRE].
Z. Bern, H. Ita, J. Parra-Martinez and M.S. Ruf, Universality in the classical limit of massless gravitational scattering, Phys. Rev. Lett. 125 (2020) 031601 [arXiv:2002.02459] [INSPIRE].
N. Moynihan and J. Murugan, On-shell electric-magnetic duality and the dual graviton, Phys. Rev. D 105 (2022) 066025 [arXiv:2002.11085] [INSPIRE].
A. Cristofoli, P.H. Damgaard, P. Di Vecchia and C. Heissenberg, Second-order Post-Minkowskian scattering in arbitrary dimensions, JHEP 07 (2020) 122 [arXiv:2003.10274] [INSPIRE].
J. Parra-Martinez, M.S. Ruf and M. Zeng, Extremal black hole scattering at \( \mathcal{O} \)(G3): graviton dominance, eikonal exponentiation, and differential equations, JHEP 11 (2020) 023 [arXiv:2005.04236] [INSPIRE].
K. Haddad and A. Helset, The double copy for heavy particles, Phys. Rev. Lett. 125 (2020) 181603 [arXiv:2005.13897] [INSPIRE].
M. Accettulli Huber, A. Brandhuber, S. De Angelis and G. Travaglini, Eikonal phase matrix, deflection angle and time delay in effective field theories of gravity, Phys. Rev. D 102 (2020) 046014 [arXiv:2006.02375] [INSPIRE].
N. Moynihan, Scattering Amplitudes and the Double Copy in Topologically Massive Theories, JHEP 12 (2020) 163 [arXiv:2006.15957] [INSPIRE].
A. Manu, D. Ghosh, A. Laddha and P.V. Athira, Soft radiation from scattering amplitudes revisited, JHEP 05 (2021) 056 [arXiv:2007.02077] [INSPIRE].
B. Sahoo, Classical Sub-subleading Soft Photon and Soft Graviton Theorems in Four Spacetime Dimensions, JHEP 12 (2020) 070 [arXiv:2008.04376] [INSPIRE].
L. de la Cruz, B. Maybee, D. O’Connell and A. Ross, Classical Yang-Mills observables from amplitudes, JHEP 12 (2020) 076 [arXiv:2009.03842] [INSPIRE].
D. Bonocore, Asymptotic dynamics on the worldline for spinning particles, JHEP 02 (2021) 007 [arXiv:2009.07863] [INSPIRE].
G. Mogull, J. Plefka and J. Steinhoff, Classical black hole scattering from a worldline quantum field theory, JHEP 02 (2021) 048 [arXiv:2010.02865] [INSPIRE].
W.T. Emond, Y.-T. Huang, U. Kol, N. Moynihan and D. O’Connell, Amplitudes from Coulomb to Kerr-Taub-NUT, JHEP 05 (2022) 055 [arXiv:2010.07861] [INSPIRE].
C. Cheung, N. Shah and M.P. Solon, Mining the Geodesic Equation for Scattering Data, Phys. Rev. D 103 (2021) 024030 [arXiv:2010.08568] [INSPIRE].
S. Mougiakakos and P. Vanhove, Schwarzschild-Tangherlini metric from scattering amplitudes in various dimensions, Phys. Rev. D 103 (2021) 026001 [arXiv:2010.08882] [INSPIRE].
J.J.M. Carrasco and I.A. Vazquez-Holm, Loop-Level Double-Copy for Massive Quantum Particles, Phys. Rev. D 103 (2021) 045002 [arXiv:2010.13435] [INSPIRE].
J.-W. Kim and M. Shim, Gravitational Dyonic Amplitude at One-Loop and its Inconsistency with the Classical Impulse, JHEP 02 (2021) 217 [arXiv:2010.14347] [INSPIRE].
N.E.J. Bjerrum-Bohr, T.V. Brown and H. Gomez, Scattering of Gravitons and Spinning Massive States from Compact Numerators, JHEP 04 (2021) 234 [arXiv:2011.10556] [INSPIRE].
R. Gonzo and A. Pokraka, Light-ray operators, detectors and gravitational event shapes, JHEP 05 (2021) 015 [arXiv:2012.01406] [INSPIRE].
L. de la Cruz, Scattering amplitudes approach to hard thermal loops, Phys. Rev. D 104 (2021) 014013 [arXiv:2012.07714] [INSPIRE].
A. Cristofoli, R. Gonzo, N. Moynihan, D. O’Connell, A. Ross, M. Sergola et al., The Uncertainty Principle and Classical Amplitudes, arXiv:2112.07556 [INSPIRE].
Y.F. Bautista and A. Laddha, Soft Constraints on KMOC Formalism, arXiv:2111.11642 [INSPIRE].
R. Aoude and A. Ochirov, Classical observables from coherent-spin amplitudes, JHEP 10 (2021) 008 [arXiv:2108.01649] [INSPIRE].
G. Cho, R.A. Porto and Z. Yang, Gravitational radiation from inspiralling compact objects: Spin effects to fourth Post-Newtonian order, arXiv:2201.05138 [INSPIRE].
Z. Bern, D. Kosmopoulos, A. Luna, R. Roiban and F. Teng, Binary Dynamics Through the Fifth Power of Spin at \( \mathcal{O} \)(G2), arXiv:2203.06202 [INSPIRE].
W.-M. Chen, M.-Z. Chung, Y.-t. Huang and J.-W. Kim, The 2PM Hamiltonian for binary Kerr to quartic in spin, JHEP 08 (2022) 148 [arXiv:2111.13639] [INSPIRE].
F. Alessio and P. Di Vecchia, Radiation reaction for spinning black-hole scattering, Phys. Lett. B 832 (2022) 137258 [arXiv:2203.13272] [INSPIRE].
A. Brandhuber, G. Chen, G. Travaglini and C. Wen, Classical gravitational scattering from a gauge-invariant double copy, JHEP 10 (2021) 118 [arXiv:2108.04216] [INSPIRE].
A. Brandhuber, G. Chen, H. Johansson, G. Travaglini and C. Wen, Kinematic Hopf Algebra for Bern-Carrasco-Johansson Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory, Phys. Rev. Lett. 128 (2022) 121601 [arXiv:2111.15649] [INSPIRE].
A. Brandhuber, G. Chen, G. Travaglini and C. Wen, A new gauge-invariant double copy for heavy-mass effective theory, JHEP 07 (2021) 047 [arXiv:2104.11206] [INSPIRE].
F. Febres Cordero, M. Kraus, G. Lin, M.S. Ruf and M. Zeng, Conservative Binary Dynamics with a Spinning Black Hole at \( \mathcal{O} \)(G3) from Scattering Amplitudes, arXiv:2205.07357 [INSPIRE].
J.F. Donoghue, Leading quantum correction to the Newtonian potential, Phys. Rev. Lett. 72 (1994) 2996 [gr-qc/9310024] [INSPIRE].
J.F. Donoghue, General relativity as an effective field theory: The leading quantum corrections, Phys. Rev. D 50 (1994) 3874 [gr-qc/9405057] [INSPIRE].
J.F. Donoghue and T. Torma, On the power counting of loop diagrams in general relativity, Phys. Rev. D 54 (1996) 4963 [hep-th/9602121] [INSPIRE].
J.F. Donoghue, B.R. Holstein, B. Garbrecht and T. Konstandin, Quantum corrections to the Reissner-Nordström and Kerr-Newman metrics, Phys. Lett. B 529 (2002) 132 [Erratum ibid. 612 (2005) 311] [hep-th/0112237] [INSPIRE].
N.E.J. Bjerrum-Bohr, J.F. Donoghue and B.R. Holstein, Quantum corrections to the Schwarzschild and Kerr metrics, Phys. Rev. D 68 (2003) 084005 [Erratum ibid. 71 (2005) 069904] [hep-th/0211071] [INSPIRE].
N.E.J. Bjerrum-Bohr, J.F. Donoghue and B.R. Holstein, Quantum gravitational corrections to the nonrelativistic scattering potential of two masses, Phys. Rev. D 67 (2003) 084033 [Erratum ibid. 71 (2005) 069903] [hep-th/0211072] [INSPIRE].
B.R. Holstein and J.F. Donoghue, Classical physics and quantum loops, Phys. Rev. Lett. 93 (2004) 201602 [hep-th/0405239] [INSPIRE].
H. Kawai, D.C. Lewellen and S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl. Phys. B 269 (1986) 1 [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, New Relations for Gauge-Theory Amplitudes, Phys. Rev. D 78 (2008) 085011 [arXiv:0805.3993] [INSPIRE].
Z. Bern, J.J.M. Carrasco and H. Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev. Lett. 105 (2010) 061602 [arXiv:1004.0476] [INSPIRE].
Z. Bern, J.J. Carrasco, M. Chiodaroli, H. Johansson and R. Roiban, The Duality Between Color and Kinematics and its Applications, arXiv:1909.01358 [INSPIRE].
R. Monteiro, D. O’Connell and C.D. White, Black holes and the double copy, JHEP 12 (2014) 056 [arXiv:1410.0239] [INSPIRE].
A. Luna, R. Monteiro, I. Nicholson, D. O’Connell and C.D. White, The double copy: Bremsstrahlung and accelerating black holes, JHEP 06 (2016) 023 [arXiv:1603.05737] [INSPIRE].
W.D. Goldberger and A.K. Ridgway, Radiation and the classical double copy for color charges, Phys. Rev. D 95 (2017) 125010 [arXiv:1611.03493] [INSPIRE].
A. Luna, R. Monteiro, I. Nicholson, A. Ochirov, D. O’Connell, N. Westerberg et al., Perturbative spacetimes from Yang-Mills theory, JHEP 04 (2017) 069 [arXiv:1611.07508] [INSPIRE].
W.D. Goldberger and A.K. Ridgway, Bound states and the classical double copy, Phys. Rev. D 97 (2018) 085019 [arXiv:1711.09493] [INSPIRE].
J. Plefka, J. Steinhoff and W. Wormsbecher, Effective action of dilaton gravity as the classical double copy of Yang-Mills theory, Phys. Rev. D 99 (2019) 024021 [arXiv:1807.09859] [INSPIRE].
W.D. Goldberger, J. Li and S.G. Prabhu, Spinning particles, axion radiation, and the classical double copy, Phys. Rev. D 97 (2018) 105018 [arXiv:1712.09250] [INSPIRE].
J. Li and S.G. Prabhu, Gravitational radiation from the classical spinning double copy, Phys. Rev. D 97 (2018) 105019 [arXiv:1803.02405] [INSPIRE].
G. Kälin and R.A. Porto, From Boundary Data to Bound States, JHEP 01 (2020) 072 [arXiv:1910.03008] [INSPIRE].
G. Kälin and R.A. Porto, From boundary data to bound states. Part II. Scattering angle to dynamical invariants (with twist), JHEP 02 (2020) 120 [arXiv:1911.09130] [INSPIRE].
C. Cheung, I.Z. Rothstein and M.P. Solon, From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion, Phys. Rev. Lett. 121 (2018) 251101 [arXiv:1808.02489] [INSPIRE].
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 (2019) 201603 [arXiv:1901.04424] [INSPIRE].
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 (2019) 024048 [arXiv:1903.05118] [INSPIRE].
A. Cristofoli, N.E.J. Bjerrum-Bohr, P.H. Damgaard and P. Vanhove, Post-Minkowskian Hamiltonians in general relativity, Phys. Rev. D 100 (2019) 084040 [arXiv:1906.01579] [INSPIRE].
B. Maybee, D. O’Connell and J. Vines, Observables and amplitudes for spinning particles and black holes, JHEP 12 (2019) 156 [arXiv:1906.09260] [INSPIRE].
A. Guevara, A. Ochirov and J. Vines, Scattering of Spinning Black Holes from Exponentiated Soft Factors, JHEP 09 (2019) 056 [arXiv:1812.06895] [INSPIRE].
M.-Z. Chung, Y.-T. Huang, J.-W. Kim and S. Lee, The simplest massive S-matrix: from minimal coupling to Black Holes, JHEP 04 (2019) 156 [arXiv:1812.08752] [INSPIRE].
E.T. Newman and A.I. Janis, Note on the Kerr spinning particle metric, J. Math. Phys. 6 (1965) 915 [INSPIRE].
N. Arkani-Hamed, Y.-t. Huang and D. O’Connell, Kerr black holes as elementary particles, JHEP 01 (2020) 046 [arXiv:1906.10100] [INSPIRE].
N. Siemonsen and J. Vines, Test black holes, scattering amplitudes and perturbations of Kerr spacetime, Phys. Rev. D 101 (2020) 064066 [arXiv:1909.07361] [INSPIRE].
R. Gonzo and C. Shi, Geodesics from classical double copy, Phys. Rev. D 104 (2021) 105012 [arXiv:2109.01072] [INSPIRE].
T. Adamo, A. Cristofoli and A. Ilderton, Classical physics from amplitudes on curved backgrounds, JHEP 08 (2022) 281 [arXiv:2203.13785] [INSPIRE].
N. Arkani-Hamed, T.-C. Huang and Y.-t. Huang, Scattering amplitudes for all masses and spins, JHEP 11 (2021) 070 [arXiv:1709.04891] [INSPIRE].
H. Johansson and A. Ochirov, Double copy for massive quantum particles with spin, JHEP 09 (2019) 040 [arXiv:1906.12292] [INSPIRE].
V. Vaidya, Gravitational spin Hamiltonians from the S matrix, Phys. Rev. D 91 (2015) 024017 [arXiv:1410.5348] [INSPIRE].
M. Chiodaroli, H. Johansson and P. Pichini, Compton black-hole scattering for s ≤ 5/2, JHEP 02 (2022) 156 [arXiv:2107.14779] [INSPIRE].
R. Aoude, K. Haddad and A. Helset, Searching for Kerr in the 2PM amplitude, JHEP 07 (2022) 072 [arXiv:2203.06197] [INSPIRE].
D. Forde, Direct extraction of one-loop integral coefficients, Phys. Rev. D 75 (2007) 125019 [arXiv:0704.1835] [INSPIRE].
F. Cachazo and A. Guevara, Leading Singularities and Classical Gravitational Scattering, JHEP 02 (2020) 181 [arXiv:1705.10262] [INSPIRE].
A. Guevara, Holomorphic Classical Limit for Spin Effects in Gravitational and Electromagnetic Scattering, JHEP 04 (2019) 033 [arXiv:1706.02314] [INSPIRE].
W.T. Emond and N. Moynihan, Scattering Amplitudes, Black Holes and Leading Singularities in Cubic Theories of Gravity, JHEP 12 (2019) 019 [arXiv:1905.08213] [INSPIRE].
G. Menezes, Leading Singularities in Higher-Derivative Yang-Mills Theory and Quadratic Gravity, Universe 8 (2022) 326 [arXiv:2205.04996] [INSPIRE].
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, JHEP 10 (2019) 206 [arXiv:1908.01493] [INSPIRE].
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 (2018) 084002 [arXiv:1709.06016] [INSPIRE].
G.U. Jakobsen, G. Mogull, J. Plefka and J. Steinhoff, SUSY in the sky with gravitons, JHEP 01 (2022) 027 [arXiv:2109.04465] [INSPIRE].
Z. Liu, R.A. Porto and Z. Yang, Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics, JHEP 06 (2021) 012 [arXiv:2102.10059] [INSPIRE].
A. Luna, I. Nicholson, D. O’Connell and C.D. White, Inelastic Black Hole Scattering from Charged Scalar Amplitudes, JHEP 03 (2018) 044 [arXiv:1711.03901] [INSPIRE].
A. Luna, R. Monteiro, D. O’Connell and C.D. White, The classical double copy for Taub-NUT spacetime, Phys. Lett. B 750 (2015) 272 [arXiv:1507.01869] [INSPIRE].
G.L. Cardoso, S. Nagy and S. Nampuri, A double copy for \( \mathcal{N} \) = 2 supergravity: a linearised tale told on-shell, JHEP 10 (2016) 127 [arXiv:1609.05022] [INSPIRE].
T. Adamo, E. Casali, L. Mason and S. Nekovar, Scattering on plane waves and the double copy, Class. Quant. Grav. 35 (2018) 015004 [arXiv:1706.08925] [INSPIRE].
A. Anastasiou, L. Borsten, M.J. Duff, S. Nagy and M. Zoccali, Gravity as Gauge Theory Squared: A Ghost Story, Phys. Rev. Lett. 121 (2018) 211601 [arXiv:1807.02486] [INSPIRE].
K. Lee, Kerr-Schild Double Field Theory and Classical Double Copy, JHEP 10 (2018) 027 [arXiv:1807.08443] [INSPIRE].
A. Luna, R. Monteiro, I. Nicholson and D. O’Connell, Type D Spacetimes and the Weyl Double Copy, Class. Quant. Grav. 36 (2019) 065003 [arXiv:1810.08183] [INSPIRE].
W. Cho and K. Lee, Heterotic Kerr-Schild Double Field Theory and Classical Double Copy, JHEP 07 (2019) 030 [arXiv:1904.11650] [INSPIRE].
H. Godazgar, M. Godazgar and C.N. Pope, Taub-NUT from the Dirac monopole, Phys. Lett. B 798 (2019) 134938 [arXiv:1908.05962] [INSPIRE].
I. Bah, R. Dempsey and P. Weck, Kerr-Schild Double Copy and Complex Worldlines, JHEP 02 (2020) 180 [arXiv:1910.04197] [INSPIRE].
R. Alawadhi, D.S. Berman, B. Spence and D. Peinador Veiga, S-duality and the double copy, JHEP 03 (2020) 059 [arXiv:1911.06797] [INSPIRE].
W.D. Goldberger and J. Li, Strings, extended objects, and the classical double copy, JHEP 02 (2020) 092 [arXiv:1912.01650] [INSPIRE].
A. Luna, S. Nagy and C. White, The convolutional double copy: a case study with a point, JHEP 09 (2020) 062 [arXiv:2004.11254] [INSPIRE].
A. Cristofoli, Gravitational shock waves and scattering amplitudes, JHEP 11 (2020) 160 [arXiv:2006.08283] [INSPIRE].
L. Borsten and S. Nagy, The pure BRST Einstein-Hilbert Lagrangian from the double-copy to cubic order, JHEP 07 (2020) 093 [arXiv:2004.14945] [INSPIRE].
E. Chacón, H. García-Compeán, A. Luna, R. Monteiro and C.D. White, New heavenly double copies, JHEP 03 (2021) 247 [arXiv:2008.09603] [INSPIRE].
H. Godazgar, M. Godazgar, R. Monteiro, D. Peinador Veiga and C.N. Pope, Weyl Double Copy for Gravitational Waves, Phys. Rev. Lett. 126 (2021) 101103 [arXiv:2010.02925] [INSPIRE].
C.D. White, Twistorial Foundation for the Classical Double Copy, Phys. Rev. Lett. 126 (2021) 061602 [arXiv:2012.02479] [INSPIRE].
D.S. Berman, K. Kim and K. Lee, The classical double copy for M-theory from a Kerr-Schild ansatz for exceptional field theory, JHEP 04 (2021) 071 [arXiv:2010.08255] [INSPIRE].
E. Lescano and J.A. Rodríguez, \( \mathcal{N} \) = 1 supersymmetric Double Field Theory and the generalized Kerr-Schild ansatz, JHEP 10 (2020) 148 [arXiv:2002.07751] [INSPIRE].
R. Monteiro, D. O’Connell, D. Peinador Veiga and M. Sergola, Classical solutions and their double copy in split signature, JHEP 05 (2021) 268 [arXiv:2012.11190] [INSPIRE].
R. Monteiro, S. Nagy, D. O’Connell, D. Peinador Veiga and M. Sergola, NS-NS spacetimes from amplitudes, JHEP 06 (2022) 021 [arXiv:2112.08336] [INSPIRE].
A. Guevara, B. Maybee, A. Ochirov, D. O’connell and J. Vines, A worldsheet for Kerr, JHEP 03 (2021) 201 [arXiv:2012.11570] [INSPIRE].
A. Falkowski and C.S. Machado, Soft Matters, or the Recursions with Massive Spinors, JHEP 05 (2021) 238 [arXiv:2005.08981] [INSPIRE].
R. Aoude, K. Haddad and A. Helset, Classical Gravitational Spinning-Spinless Scattering at \( \mathcal{O} \)(G2S∞), Phys. Rev. Lett. 129 (2022) 141102 [arXiv:2205.02809] [INSPIRE].
W.-M. Chen, M.-Z. Chung, Y.-t. Huang and J.-W. Kim, Lense-Thirring effects from on-shell amplitudes, arXiv:2205.07305 [INSPIRE].
A. Guevara, A. Ochirov and J. Vines, Black-hole scattering with general spin directions from minimal-coupling amplitudes, Phys. Rev. D 100 (2019) 104024 [arXiv:1906.10071] [INSPIRE].
N. Moynihan, Kerr-Newman from Minimal Coupling, JHEP 01 (2020) 014 [arXiv:1909.05217] [INSPIRE].
U. Kol, D. O’connell and O. Telem, The radial action from probe amplitudes to all orders, JHEP 03 (2022) 141 [arXiv:2109.12092] [INSPIRE].
Y.-T. Huang, U. Kol and D. O’Connell, Double copy of electric-magnetic duality, Phys. Rev. D 102 (2020) 046005 [arXiv:1911.06318] [INSPIRE].
C. Heissenberg, Infrared divergences and the eikonal exponentiation, Phys. Rev. D 104 (2021) 046016 [arXiv:2105.04594] [INSPIRE].
M. Ciafaloni, D. Colferai and G. Veneziano, Infrared features of gravitational scattering and radiation in the eikonal approach, Phys. Rev. D 99 (2019) 066008 [arXiv:1812.08137] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, Universality of ultra-relativistic gravitational scattering, Phys. Lett. B 811 (2020) 135924 [arXiv:2008.12743] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, Radiation Reaction from Soft Theorems, Phys. Lett. B 818 (2021) 136379 [arXiv:2101.05772] [INSPIRE].
G.U. Jakobsen, G. Mogull, J. Plefka and J. Steinhoff, Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory, Phys. Rev. Lett. 126 (2021) 201103 [arXiv:2101.12688] [INSPIRE].
C. Shi and J. Plefka, Classical double copy of worldline quantum field theory, Phys. Rev. D 105 (2022) 026007 [arXiv:2109.10345] [INSPIRE].
P.H. Damgaard, L. Plante and P. Vanhove, On an exponential representation of the gravitational S-matrix, JHEP 11 (2021) 213 [arXiv:2107.12891] [INSPIRE].
W.T. Emond, N. Moynihan and L. Wei, Quantization conditions and the double copy, JHEP 09 (2022) 108 [arXiv:2109.11531] [INSPIRE].
P. Di Vecchia, C. Heissenberg, R. Russo and G. Veneziano, The eikonal operator at arbitrary velocities I: the soft-radiation limit, JHEP 07 (2022) 039 [arXiv:2204.02378] [INSPIRE].
J.D. Jackson, Classical Electrodynamics, Wiley (1998) [ISBN: 9780471309321].
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Menezes, G., Sergola, M. NLO deflections for spinning particles and Kerr black holes. J. High Energ. Phys. 2022, 105 (2022). https://doi.org/10.1007/JHEP10(2022)105
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DOI: https://doi.org/10.1007/JHEP10(2022)105