Abstract
We develop an Effective Field Theory (EFT) formalism to solve for the conservative dynamics of binary systems in gravity via Post-Minkowskian (PM) scattering data. Our framework combines a systematic EFT approach to compute the deflection angle in the PM expansion, together with the ‘Boundary-to-Bound’ (B2B) dictionary introduced in [1, 2]. Due to the nature of scattering processes, a remarkable reduction of complexity occurs both in the number of Feynman diagrams and type of integrals, compared to a direct EFT computation of the potential in a PM scheme. We provide two illustrative examples. Firstly, we compute all the conservative gravitational observables for bound orbits to 2PM, which follow from only one topology beyond leading order. The results agree with those in [1, 2], obtained through the ‘impetus formula’ applied to the classical limit of the one loop amplitude in Cheung et al. [3]. For the sake of comparison we reconstruct the conservative Hamiltonian to 2PM order, which is equivalent to the one derived in [3] from a matching calculation. Secondly, we compute the scattering angle due to tidal effects from the electric- and magnetic-type Love numbers at leading PM order. Using the B2B dictionary we then obtain the tidal contribution to the periastron advance. We also construct a Hamiltonian including tidal effects at leading PM order. Although relying on (relativistic) Feynman diagrams, the EFT formalism developed here does not involve taking the classical limit of a quantum amplitude, neither integrals with internal massive fields, nor additional matching calculations, nor spurious (‘super-classical’) infrared singularities. By construction, the EFT approach can be automatized to all PM orders.
Article PDF
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
Avoid common mistakes on your manuscript.
References
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].
LIGO Scientific and Virgo collaborations, Open data from the first and second observing runs of advanced LIGO and advanced Virgo, arXiv:1912.11716 [INSPIRE].
A. Buonanno and B.S. Sathyaprakash, Sources of gravitational waves: theory and observations, in General relativity and gravitation: a centennial perspective, Cambridge University Press, Cambridge, U.K. (2014), pg. 287 [arXiv:1410.7832] [INSPIRE].
R.A. Porto, The tune of love and the nature(ness) of spacetime, Fortsch. Phys. 64 (2016) 723 [arXiv:1606.08895] [INSPIRE].
R.A. Porto, The music of the spheres: the dawn of gravitational wave science, arXiv:1703.06440 [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].
W.D. Goldberger, Les Houches lectures on effective field theories and gravitational radiation, in Les Houches summer school — Session 86. Particle physics and cosmology: the fabric of spacetime, (2007) [hep-ph/0701129] [INSPIRE].
R.A. Porto and R. Sturani, Scalar gravity: post-Newtonian corrections via an effective field theory approach, in Les Houches summer school — session 86. Particle physics and cosmology: the fabric of spacetime, (2007) [gr-qc/0701105] [INSPIRE].
S. Foffa and R. Sturani, Effective field theory methods to model compact binaries, Class. Quant. Grav. 31 (2014) 043001 [arXiv:1309.3474] [INSPIRE].
I.Z. Rothstein, Progress in effective field theory approach to the binary inspiral problem, Gen. Rel. Grav. 46 (2014) 1726 [INSPIRE].
V. Cardoso and R.A. Porto, Analytic approximations, perturbation theory, effective field theory methods and their applications, Gen. Rel. Grav. 46 (2014) 1682 [arXiv:1401.2193] [INSPIRE].
R.A. Porto, The effective field theorist’s approach to gravitational dynamics, Phys. Rept. 633 (2016) 1 [arXiv:1601.04914] [INSPIRE].
M. Beneke and V.A. Smirnov, Asymptotic expansion of Feynman integrals near threshold, Nucl. Phys. B 522 (1998) 321 [hep-ph/9711391] [INSPIRE].
R.A. Porto, Lamb shift and the gravitational binding energy for binary black holes, Phys. Rev. D 96 (2017) 024063 [arXiv:1703.06434] [INSPIRE].
R.A. Porto and I.Z. Rothstein, Apparent ambiguities in the post-Newtonian expansion for binary systems, Phys. Rev. D 96 (2017) 024062 [arXiv:1703.06433] [INSPIRE].
L. Blanchet, Gravitational radiation from post-Newtonian sources and inspiralling compact binaries, Living Rev. Rel. 17 (2014) 2 [arXiv:1310.1528] [INSPIRE].
G. Schäfer and P. Jaranowski, Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries, Living Rev. Rel. 21 (2018) 7 [arXiv:1805.07240] [INSPIRE].
T. Damour, P. Jaranowski and G. Schäfer, Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems, Phys. Rev. D 89 (2014) 064058 [arXiv:1401.4548] [INSPIRE].
P. Jaranowski and G. Schäfer, Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries, Phys. Rev. D 92 (2015) 124043 [arXiv:1508.01016] [INSPIRE].
L. Bernard, L. Blanchet, A. Bohé, G. Faye and S. Marsat, Fokker action of nonspinning compact binaries at the fourth post-Newtonian approximation, Phys. Rev. D 93 (2016) 084037 [arXiv:1512.02876] [INSPIRE].
L. Bernard, L. Blanchet, A. Bohé, G. Faye and S. Marsat, Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order, Phys. Rev. D 96 (2017) 104043 [arXiv:1706.08480] [INSPIRE].
T. Marchand, L. Bernard, L. Blanchet and G. Faye, Ambiguity-free completion of the equations of motion of compact binary systems at the fourth post-Newtonian order, Phys. Rev. D 97 (2018) 044023 [arXiv:1707.09289] [INSPIRE].
J.B. Gilmore and A. Ross, Effective field theory calculation of second post-Newtonian binary dynamics, Phys. Rev. D 78 (2008) 124021 [arXiv:0810.1328] [INSPIRE].
S. Foffa and R. Sturani, Effective field theory calculation of conservative binary dynamics at third post-Newtonian order, Phys. Rev. D 84 (2011) 044031 [arXiv:1104.1122] [INSPIRE].
S. Foffa and R. Sturani, Dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant, Phys. Rev. D 87 (2013) 064011 [arXiv:1206.7087] [INSPIRE].
C.R. Galley, A.K. Leibovich, R.A. Porto and A. Ross, Tail effect in gravitational radiation reaction: time nonlocality and renormalization group evolution, Phys. Rev. D 93 (2016) 124010 [arXiv:1511.07379] [INSPIRE].
S. Foffa, P. Mastrolia, R. Sturani and C. Sturm, Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant, Phys. Rev. D 95 (2017) 104009 [arXiv:1612.00482] [INSPIRE].
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 (2019) 024047 [arXiv:1903.05113] [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].
W.D. Goldberger and I.Z. Rothstein, Dissipative effects in the worldline approach to black hole dynamics, Phys. Rev. D 73 (2006) 104030 [hep-th/0511133] [INSPIRE].
W.D. Goldberger and A. Ross, Gravitational radiative corrections from effective field theory, Phys. Rev. D 81 (2010) 124015 [arXiv:0912.4254] [INSPIRE].
A. Ross, Multipole expansion at the level of the action, Phys. Rev. D 85 (2012) 125033 [arXiv:1202.4750] [INSPIRE].
C.R. Galley and A.K. Leibovich, Radiation reaction at 3.5 post-Newtonian order in effective field theory, Phys. Rev. D 86 (2012) 044029 [arXiv:1205.3842] [INSPIRE].
A.K. Leibovich, N.T. Maia, I.Z. Rothstein and Z. Yang, Second post-Newtonian order radiative dynamics of inspiralling compact binaries in the effective field theory approach, Phys. Rev. D 101 (2020) 084058 [arXiv:1912.12546] [INSPIRE].
R.A. Porto, Post-Newtonian corrections to the motion of spinning bodies in NRGR, Phys. Rev. D 73 (2006) 104031 [gr-qc/0511061] [INSPIRE].
R.A. Porto and I.Z. Rothstein, The hyperfine Einstein-Infeld-Hoffmann potential, Phys. Rev. Lett. 97 (2006) 021101 [gr-qc/0604099] [INSPIRE].
R.A. Porto, New results at 3PN via an effective field theory of gravity, in 11th Marcel Grossmann Meeting on General Relativity, World Scientific, Singapore (2007), pg. 2493 [gr-qc/0701106] [INSPIRE].
R.A. Porto and I.Z. Rothstein, Comment on ‘on the next-to-leading order gravitational spin(1)-spin(2) dynamics’ by J. Steinhoff et al., arXiv:0712.2032 [INSPIRE].
R.A. Porto, Absorption effects due to spin in the worldline approach to black hole dynamics, Phys. Rev. D 77 (2008) 064026 [arXiv:0710.5150] [INSPIRE].
R.A. Porto and I.Z. Rothstein, spin(1)spin(2) effects in the motion of inspiralling compact binaries at third order in the post-Newtonian expansion, Phys. Rev. D 78 (2008) 044012 [Erratum ibid. 81 (2010) 029904] [arXiv:0802.0720] [INSPIRE].
R.A. Porto and I.Z. Rothstein, Next to leading order spin(1)spin(1) effects in the motion of inspiralling compact binaries, Phys. Rev. D 78 (2008) 044013 [Erratum ibid. 81 (2010) 029905] [arXiv:0804.0260] [INSPIRE].
R.A. Porto, Next to leading order spin-orbit effects in the motion of inspiralling compact binaries, Class. Quant. Grav. 27 (2010) 205001 [arXiv:1005.5730] [INSPIRE].
R.A. Porto, A. Ross and I.Z. Rothstein, Spin induced multipole moments for the gravitational wave flux from binary inspirals to third post-Newtonian order, JCAP 03 (2011) 009 [arXiv:1007.1312] [INSPIRE].
R.A. Porto, A. Ross and I.Z. Rothstein, Spin induced multipole moments for the gravitational wave amplitude from binary inspirals to 2.5 post-Newtonian order, JCAP 09 (2012) 028 [arXiv:1203.2962] [INSPIRE].
N.T. Maia, C.R. Galley, A.K. Leibovich and R.A. Porto, Radiation reaction for spinning bodies in effective field theory I: spin-orbit effects, Phys. Rev. D 96 (2017) 084064 [arXiv:1705.07934] [INSPIRE].
N.T. Maia, C.R. Galley, A.K. Leibovich and R.A. Porto, Radiation reaction for spinning bodies in effective field theory II: spin-spin effects, Phys. Rev. D 96 (2017) 084065 [arXiv:1705.07938] [INSPIRE].
M. Levi and J. Steinhoff, Complete conservative dynamics for inspiralling compact binaries with spins at fourth post-Newtonian order, arXiv:1607.04252 [INSPIRE].
M. Levi, A.J. Mcleod and M. Von Hippel, N3 LO gravitational spin-orbit coupling at order G4, arXiv:2003.02827 [INSPIRE].
M. Levi, A.J. Mcleod and M. Von Hippel, NNNLO gravitational quadratic-in-spin interactions at the quartic order in G, arXiv:2003.07890 [INSPIRE].
S. Foffa, P. Mastrolia, R. Sturani, C. Sturm and W.J. Torres Bobadilla, Static two-body potential at fifth post-Newtonian order, Phys. Rev. Lett. 122 (2019) 241605 [arXiv:1902.10571] [INSPIRE].
J. Blümlein, A. Maier and P. Marquard, Five-loop static contribution to the gravitational interaction potential of two point masses, Phys. Lett. B 800 (2020) 135100 [arXiv:1902.11180] [INSPIRE].
S. Foffa and R. Sturani, Hereditary terms at next-to-leading order in two-body gravitational dynamics, Phys. Rev. D 101 (2020) 064033 [arXiv:1907.02869] [INSPIRE].
L. Blanchet, S. Foffa, F. Larrouturou and R. Sturani, Logarithmic tail contributions to the energy function of circular compact binaries, Phys. Rev. D 101 (2020) 084045 [arXiv:1912.12359] [INSPIRE].
S. Foffa, Gravitating binaries at 5PN in the post-Minkowskian approximation, Phys. Rev. D 89 (2014) 024019 [arXiv:1309.3956] [INSPIRE].
Y. Iwasaki, Quantum theory of gravitation vs. classical theory — fourth-order potential, Prog. Theor. Phys. 46 (1971) 1587 [INSPIRE].
J.J.M. Carrasco, Gauge and gravity amplitude relations, in Theoretical Advanced Study Institute in Elementary Particle Physics. Journeys through the precision frontier: amplitudes for colliders, World Scientific, Singapore (2015), pg. 477 [arXiv:1506.00974] [INSPIRE].
H. Elvang and Y.-T. Huang, Scattering amplitudes in gauge theory and gravity, Cambridge University Press, Cambridge, U.K. (2015).
C. Cheung, TASI lectures on scattering amplitudes, in Proceedings, Theoretical Advanced Study Institute in Elementary Particle Physics: anticipating the next discoveries in particle physics (TASI 2016), Boulder, CO, U.S.A., 6 June–1 July 2016, R. Essig and I. Low eds., World Scientific, Singapore (2018), pg. 571 [arXiv:1708.03872] [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].
D. Neill and I.Z. Rothstein, Classical space-times from the S matrix, Nucl. Phys. B 877 (2013) 177 [arXiv:1304.7263] [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].
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].
D.A. Kosower, B. Maybee and D. O’Connell, Amplitudes, observables, and classical scattering, JHEP 02 (2019) 137 [arXiv:1811.10950] [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].
C.R. Galley and R.A. Porto, Gravitational self-force in the ultra-relativistic limit: the “large-N ” expansion, JHEP 11 (2013) 096 [arXiv:1302.4486] [INSPIRE].
B.R. Holstein and A. Ross, Spin effects in long range gravitational scattering, arXiv:0802.0716 [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].
V. Vaidya, Gravitational spin Hamiltonians from the S matrix, Phys. Rev. D 91 (2015) 024017 [arXiv:1410.5348] [INSPIRE].
A. Guevara, Holomorphic classical limit for spin effects in gravitational and electromagnetic scattering, JHEP 04 (2019) 033 [arXiv:1706.02314] [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].
A. Guevara, A. Ochirov and J. Vines, Scattering of spinning black holes from exponentiated soft factors, JHEP 09 (2019) 056 [arXiv:1812.06895] [INSPIRE].
S. Caron-Huot and Z. Zahraee, Integrability of black hole orbits in maximal supergravity, JHEP 07 (2019) 179 [arXiv:1810.04694] [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.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].
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].
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.E.J. Bjerrum-Bohr, A. Cristofoli and P.H. Damgaard, Post-Minkowskian scattering angle in Einstein gravity, JHEP 08 (2020) 038 [arXiv:1910.09366] [INSPIRE].
M.-Z. Chung, Y.-T. Huang and J.-W. Kim, Classical potential for general spinning bodies, JHEP 09 (2020) 074 [arXiv:1908.08463] [INSPIRE].
Y.F. Bautista and A. Guevara, From scattering amplitudes to classical physics: universality, double copy and soft theorems, arXiv:1903.12419 [INSPIRE].
Y.F. Bautista and A. Guevara, On the double copy for spinning matter, arXiv:1908.11349 [INSPIRE].
A. Koemans Collado, P. Di Vecchia and R. Russo, Revisiting the second post-Minkowskian eikonal and the dynamics of binary black holes, Phys. Rev. D 100 (2019) 066028 [arXiv:1904.02667] [INSPIRE].
H. Johansson and A. Ochirov, Double copy for massive quantum particles with spin, JHEP 09 (2019) 040 [arXiv:1906.12292] [INSPIRE].
R. Aoude, K. Haddad and A. Helset, On-shell heavy particle effective theories, JHEP 05 (2020) 051 [arXiv:2001.09164] [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].
M.-Z. Chung, Y.-T. Huang, J.-W. Kim and S. Lee, Complete Hamiltonian for spinning binary systems at first post-Minkowskian order, JHEP 05 (2020) 105 [arXiv:2003.06600] [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].
Z. Bern, A. Luna, R. Roiban, C.-H. Shen and M. Zeng, Spinning black hole binary dynamics, scattering amplitudes and effective field theory, arXiv:2005.03071 [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].
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 (2019) 104004 [arXiv:1901.07102] [INSPIRE].
T. Damour and A. Nagar, The effective-one-body approach to the general relativistic two body problem, Lect. Notes Phys. 905 (2016) 273 [INSPIRE].
T. Damour, Gravitational scattering, post-Minkowskian approximation and effective one-body theory, Phys. Rev. D 94 (2016) 104015 [arXiv:1609.00354] [INSPIRE].
T. Damour, High-energy gravitational scattering and the general relativistic two-body problem, Phys. Rev. D 97 (2018) 044038 [arXiv:1710.10599] [INSPIRE].
D. Bini, T. Damour and A. Geralico, Novel approach to binary dynamics: application to the fifth post-Newtonian level, Phys. Rev. Lett. 123 (2019) 231104 [arXiv:1909.02375] [INSPIRE].
T. Damour, Classical and quantum scattering in post-Minkowskian gravity, Phys. Rev. D 102 (2020) 024060 [arXiv:1912.02139] [INSPIRE].
D. Bini, T. Damour and A. Geralico, Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders, Phys. Rev. D 102 (2020) 024062 [arXiv:2003.11891] [INSPIRE].
D. Bini, T. Damour and A. Geralico, Sixth post-Newtonian local-in-time dynamics of binary systems, Phys. Rev. D 102 (2020) 024061 [arXiv:2004.05407] [INSPIRE].
J. Vines, J. Steinhoff and A. Buonanno, Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order, Phys. Rev. D 99 (2019) 064054 [arXiv:1812.00956] [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].
D. Bini, T. Damour and A. Geralico, Scattering of tidally interacting bodies in post-Minkowskian gravity, Phys. Rev. D 101 (2020) 044039 [arXiv:2001.00352] [INSPIRE].
T. Damour, P. Jaranowski and G. Schäfer, Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation, Phys. Rev. D 62 (2000) 044024 [gr-qc/9912092] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys. B 425 (1994) 217 [hep-ph/9403226] [INSPIRE].
Z. Bern, L.J. Dixon, D.C. Dunbar and D.A. Kosower, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys. B 435 (1995) 59 [hep-ph/9409265] [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].
C. Cheung and M.P. Solon, Classical gravitational scattering at \( \mathcal{O} \)(G3) from Feynman diagrams, JHEP 06 (2020) 144 [arXiv:2003.08351] [INSPIRE].
G. Kälin, Z. Liu and R.A. Porto, Conservative dynamics of binary systems to third post-Minkowskian order from the effective field theory approach, arXiv:2007.04977 [INSPIRE].
V.A. Smirnov, Analytic tools for Feynman integrals, Springer Tracts Mod. Phys. 250 (2012) [INSPIRE].
C. Cheung and G.N. Remmen, Hidden simplicity of the gravity action, JHEP 09 (2017) 002 [arXiv:1705.00626] [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 et al., Perturbative spacetimes from Yang-Mills theory, JHEP 04 (2017) 069 [arXiv:1611.07508] [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].
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. Li and S.G. Prabhu, Gravitational radiation from the classical spinning double copy, Phys. Rev. D 97 (2018) 105019 [arXiv:1803.02405] [INSPIRE].
C.-H. Shen, Gravitational radiation from color-kinematics duality, JHEP 11 (2018) 162 [arXiv:1806.07388] [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].
J. Plefka, C. Shi, J. Steinhoff and T. Wang, Breakdown of the classical double copy for the effective action of dilaton-gravity at NNLO, Phys. Rev. D 100 (2019) 086006 [arXiv:1906.05875] [INSPIRE].
K. Kim, K. Lee, R. Monteiro, I. Nicholson and D. Peinador Veiga, The classical double copy of a point charge, JHEP 02 (2020) 046 [arXiv:1912.02177] [INSPIRE].
W.D. Goldberger and J. Li, Strings, extended objects, and the classical double copy, JHEP 02 (2020) 092 [arXiv:1912.01650] [INSPIRE].
L. Alfonsi, C.D. White and S. Wikeley, Topology and Wilson lines: global aspects of the double copy, JHEP 07 (2020) 091 [arXiv:2004.07181] [INSPIRE].
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 (2012) 064039 [arXiv:1111.5378] [INSPIRE].
O.B. Firsov, Determination of the forces acting between atoms using the differential effective cross-section for elastic scattering, Zh. Eksp. Teor. Fiz. 24 (1953) 279.
A. Kuntz, Half-solution to the two-body problem in general relativity, Phys. Rev. D 102 (2020) 064019 [arXiv:2003.03366] [INSPIRE].
S. Rafie-Zinedine, Simplifying quantum gravity calculations, master’s thesis, Lund U., Lund, Sweden (2018) [arXiv:1808.06086] [INSPIRE].
R. Akhoury, R. Saotome and G. Sterman, High energy scattering in perturbative quantum gravity at next to leading power, arXiv:1308.5204 [INSPIRE].
R. Saotome and R. Akhoury, Relationship between gravity and gauge scattering in the high energy limit, JHEP 01 (2013) 123 [arXiv:1210.8111] [INSPIRE].
B. Grinstein, Lectures on heavy quark effective theory, in Workshop on high-energy phenomenology (CINVESTAV), (1991), pg. 0161 [INSPIRE].
K. Westpfahl, High-speed scattering of charged and uncharged particles in general relativity, Fortsch. Phys. 33 (1985) 417 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2006.01184
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Kälin, G., Porto, R.A. Post-Minkowskian effective field theory for conservative binary dynamics. J. High Energ. Phys. 2020, 106 (2020). https://doi.org/10.1007/JHEP11(2020)106
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2020)106