Abstract
We confirm the generalized actions of the complete NLO cubic-in-spin interactions for generic compact binaries which were first tackled via an extension of the EFT of spinning gravitating objects. We first reduce these generalized actions to standard actions with spins, where the interaction potentials are found to consist of 6 independent sectors, including a new unique sector that is proportional to the square of the quadrupolar deformation parameter, \( {C}_{{\textrm{ES}}^2} \). We derive the general Hamiltonians in an arbitrary reference frame, and for generic kinematic configurations. With these most general Hamiltonians we construct the full Poincaré algebra of all the sectors at the fourth and a half post-Newtonian (4.5PN) order, including the third subleading spin-orbit sector, recently accomplished uniquely via our framework, thus proving the Poincaré invariance of all relevant sectors. We then derive the binding energies with gauge-invariant relations useful for gravitational-wave applications. Finally, we also derive the extrapolated scattering angles in the aligned-spins configuration for the scattering problem. Yet, as made clear already as of quadratic-in-spin sectors, the aligned-spins simplification inherent to the scattering-angle observable, entails a great loss of physical information, that is only growing with higher-spin sectors. Our completion of the full Poincaré algebra at the present 4.5PN order provides strong confidence that this new precision frontier in PN theory has now been established.
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LIGO Scientific and Virgo collaborations, GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, Phys. Rev. X 9 (2019) 031040 [arXiv:1811.12907] [INSPIRE].
LIGO Scientific and Virgo collaborations, GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run, Phys. Rev. X 11 (2021) 021053 [arXiv:2010.14527] [INSPIRE].
LIGO Scientific et al. collaborations, GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run, arXiv:2111.03606 [INSPIRE].
LIGO Scientific collaboration, Advanced LIGO, Class. Quant. Grav. 32 (2015) 074001 [arXiv:1411.4547] [INSPIRE].
VIRGO collaboration, Advanced Virgo: a second-generation interferometric gravitational wave detector, Class. Quant. Grav. 32 (2015) 024001 [arXiv:1408.3978] [INSPIRE].
KAGRA collaboration, Overview of KAGRA: Detector design and construction history, PTEP 2021 (2021) 05A101 [arXiv:2005.05574] [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, GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral, Phys. Rev. Lett. 119 (2017) 161101 [arXiv:1710.05832] [INSPIRE].
LIGO Scientific et al. collaborations, Observation of Gravitational Waves from Two Neutron Star-Black Hole Coalescences, Astrophys. J. Lett. 915 (2021) L5 [arXiv:2106.15163] [INSPIRE].
L. Blanchet, Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries, Living Rev. Rel. 17 (2014) 2 [arXiv:1310.1528] [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].
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].
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 et al., Gravitational dynamics at O(G6): perturbative gravitational scattering meets experimental mathematics, arXiv:2008.09389 [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].
J. Blümlein, A. Maier, P. Marquard and G. Schäfer, The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions, Nucl. Phys. B 965 (2021) 115352 [arXiv:2010.13672] [INSPIRE].
W.D. Goldberger, Effective field theories of gravity and compact binary dynamics: A Snowmass 2021 whitepaper, in the proceedings of the Snowmass 2021, Seattle U.S.A., July 17–26 (2022) [arXiv:2206.14249] [INSPIRE].
A. Antonelli et al., Gravitational spin-orbit coupling through third-subleading post-Newtonian order: from first-order self-force to arbitrary mass ratios, Phys. Rev. Lett. 125 (2020) 011103 [arXiv:2003.11391] [INSPIRE].
A. Antonelli et al., Gravitational spin-orbit and aligned spin1-spin2 couplings through third-subleading post-Newtonian orders, Phys. Rev. D 102 (2020) 124024 [arXiv:2010.02018] [INSPIRE].
M. Levi and J. Steinhoff, Spinning gravitating objects in the effective field theory in the post-Newtonian scheme, JHEP 09 (2015) 219 [arXiv:1501.04956] [INSPIRE].
M. Levi and J. Steinhoff, EFTofPNG: A package for high precision computation with the Effective Field Theory of Post-Newtonian Gravity, Class. Quant. Grav. 34 (2017) 244001 [arXiv:1705.06309] [INSPIRE].
M. Levi, A.J. Mcleod and M. Von Hippel, N3LO gravitational spin-orbit coupling at order G4, JHEP 07 (2021) 115 [arXiv:2003.02827] [INSPIRE].
J.-W. Kim, M. Levi and Z. Yin, N3LO spin-orbit interaction via the EFT of spinning gravitating objects, JHEP 05 (2023) 184 [arXiv:2208.14949] [INSPIRE].
B.M. Barker and R.F. O’Connell, Gravitational Two-Body Problem with Arbitrary Masses, Spins, and Quadrupole Moments, Phys. Rev. D 12 (1975) 329 [INSPIRE].
M. Levi and J. Steinhoff, Leading order finite size effects with spins for inspiralling compact binaries, JHEP 06 (2015) 059 [arXiv:1410.2601] [INSPIRE].
X. Bekaert et al., Snowmass White Paper: Higher Spin Gravity and Higher Spin Symmetry, arXiv:2205.01567 [INSPIRE].
M. Levi, S. Mougiakakos and M. Vieira, Gravitational cubic-in-spin interaction at the next-to-leading post-Newtonian order, JHEP 01 (2021) 036 [arXiv:1912.06276] [INSPIRE].
M. Levi, Effective Field Theories of Post-Newtonian Gravity: A comprehensive review, Rept. Prog. Phys. 83 (2020) 075901 [arXiv:1807.01699] [INSPIRE].
M. Levi, Binary dynamics from spin1-spin2 coupling at fourth post-Newtonian order, Phys. Rev. D 85 (2012) 064043 [arXiv:1107.4322] [INSPIRE].
M. Levi and J. Steinhoff, Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme, JCAP 01 (2016) 011 [arXiv:1506.05056] [INSPIRE].
M. Levi and J. Steinhoff, Next-to-next-to-leading order gravitational spin-squared potential via the effective field theory for spinning objects in the post-Newtonian scheme, JCAP 01 (2016) 008 [arXiv:1506.05794] [INSPIRE].
M. Levi and J. Steinhoff, Complete conservative dynamics for inspiralling compact binaries with spins at the fourth post-Newtonian order, JCAP 09 (2021) 029 [arXiv:1607.04252] [INSPIRE].
M. Levi, A.J. Mcleod and M. Von Hippel, N3LO gravitational quadratic-in-spin interactions at G4, JHEP 07 (2021) 116 [arXiv:2003.07890] [INSPIRE].
J.-W. Kim, M. Levi and Z. Yin, Quadratic-in-spin interactions at fifth post-Newtonian order probe new physics, Phys. Lett. B 834 (2022) 137410 [arXiv:2112.01509] [INSPIRE].
J.-W. Kim, M. Levi and Z. Yin, N3LO quadratic-in-spin interactions for generic compact binaries, JHEP 03 (2023) 098 [arXiv:2209.09235] [INSPIRE].
M. Levi and Z. Yin, Completing the fifth PN precision frontier via the EFT of spinning gravitating objects, JHEP 04 (2023) 079 [arXiv:2211.14018] [INSPIRE].
M.K. Mandal, P. Mastrolia, R. Patil and J. Steinhoff, Gravitational quadratic-in-spin Hamiltonian at NNNLO in the post-Newtonian framework, JHEP 07 (2023) 128 [arXiv:2210.09176] [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].
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].
Z. Bern et al., Binary Dynamics Through the Fifth Power of Spin at \( \mathcal{O} \)(G2), Phys. Rev. Lett. 130 (2023) 201402 [arXiv:2203.06202] [INSPIRE].
M. Levi and F. Teng, NLO gravitational quartic-in-spin interaction, JHEP 01 (2021) 066 [arXiv:2008.12280] [INSPIRE].
A.J. Hanson and T. Regge, The Relativistic Spherical Top, Annals Phys. 87 (1974) 498 [INSPIRE].
I. Bailey and W. Israel, Lagrangian Dynamics of Spinning Particles and Polarized Media in General Relativity, Commun. Math. Phys. 42 (1975) 65 [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].
W. Tulczyjew, Motion of multipole particles in general relativity theory, Acta Phys.Polon. 18 (1959) 393.
K. Yee and M. Bander, Equations of motion for spinning particles in external electromagnetic and gravitational fields, Phys. Rev. D 48 (1993) 2797 [hep-th/9302117] [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].
M. Levi, Next to Leading Order gravitational Spin-Orbit coupling in an Effective Field Theory approach, Phys. Rev. D 82 (2010) 104004 [arXiv:1006.4139] [INSPIRE].
M. Levi, Next to Leading Order gravitational spin1-spin2 coupling with Kaluza-Klein reduction, Phys. Rev. D 82 (2010) 064029 [arXiv:0802.1508] [INSPIRE].
M.H.L. Pryce, The Mass center in the restricted theory of relativity and its connection with the quantum theory of elementary particles, Proc. Roy. Soc. Lond. A 195 (1948) 62 [INSPIRE].
T.D. Newton and E.P. Wigner, Localized States for Elementary Systems, Rev. Mod. Phys. 21 (1949) 400 [INSPIRE].
M. Levi and J. Steinhoff, Equivalence of ADM Hamiltonian and Effective Field Theory approaches at next-to-next-to-leading order spin1-spin2 coupling of binary inspirals, JCAP 12 (2014) 003 [arXiv:1408.5762] [INSPIRE].
R. Morales, High-Precision Gravity Observables: From EFTs to Particle Amplitudes, MSc thesis, Univerity of Copenhagen, Denmark (2021).
L. Bel and J. Martin, Predictive relativistic mechanics of systems of N particles with spin, Ann. Inst. H. Poincaré Phys. Théor. 33 (1980) 409.
M.K. Mandal, P. Mastrolia, R. Patil and J. Steinhoff, Gravitational spin-orbit Hamiltonian at NNNLO in the post-Newtonian framework, JHEP 03 (2023) 130 [arXiv:2209.00611] [INSPIRE].
A. Edison and M. Levi, A tale of tails through generalized unitarity, Phys. Lett. B 837 (2023) 137634 [arXiv:2202.04674] [INSPIRE].
T. Damour and G. Schaefer, Higher Order Relativistic Periastron Advances and Binary Pulsars, Nuovo Cim. B 101 (1988) 127 [INSPIRE].
Acknowledgments
We thank Fei Teng for pleasant discussions. ML has been supported by the Science and Technology Facilities Council (STFC) Rutherford Grant ST/V003895/2 “Harnessing QFT for Gravity”, and by the Mathematical Institute University of Oxford. ZY is supported by the Knut and Alice Wallenberg Foundation under grants KAW 2018.0116 and KAW 2018.0162.
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Levi, M., Morales, R. & Yin, Z. From the EFT of spinning gravitating objects to Poincaré and gauge invariance at the 4.5PN precision frontier. J. High Energ. Phys. 2023, 90 (2023). https://doi.org/10.1007/JHEP09(2023)090
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DOI: https://doi.org/10.1007/JHEP09(2023)090