Complete Hamiltonian for spinning binary systems at first post-Minkowskian order
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Springer
Received: March 25, 2020 Accepted: April 28, 2020 Published: May 22, 2020
Complete Hamiltonian for spinning binary systems at first post-Minkowskian order
a
Department of Physics and Astronomy, National Taiwan University, Taipei 10617, Taiwan b Physics Division, National Center for Theoretical Sciences, National Tsing-Hua University, No. 101, section 2, Kuang-Fu Road, Hsinchu, Taiwan c Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea d Center for Theoretical Physics, Seoul National University, Seoul 08826, Korea e College of Liberal Studies, Seoul National University, Seoul 08826, Korea
E-mail: [email protected], [email protected], [email protected], [email protected] Abstract: Building upon recent progress in applying on-shell amplitude techniques to classical observables in general relativity, we propose a closed-form formula for the conservative Hamiltonian of a spinning binary system at the 1st post-Minkowskian (1PM) order. It is applicable for general compact spinning bodies with arbitrary spin multipole moments. The formula is linear in gravitational constant by definition, but exact to all orders in momentum and spin expansions. At each spin order, our formula implies that the spin-dependence and momentum dependence factorize almost completely. We expand our formula in momentum and compare the terms with 1PM parts of the post-Newtonian computations in the literature. Up to canonical transformations, our results agree perfectly with all previous ones. We also compare our formula for black hole to that derived from a spinning test-body near a Kerr black hole via the effective one-body mapping, and find perfect agreement. Keywords: Black Holes, Scattering Amplitudes ArXiv ePrint: 2003.06600
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)105
JHEP05(2020)105
Ming-Zhi Chung,a Yu-tin Huang,a,b Jung-Wook Kimc and Sangmin Leec,d,e
Contents 1
2 Complete 1PM potential from amplitude 2.1 The kinematics 2.2 1PM amplitude 2.3 Thomas-Wigner rotation 2.4 Complete 1PM potential
4 4 5 7 9
3 1PM potential at each spin order 3.1 Linear in spin 3.2 Quadratic in spin 3.3 Cubic in spin 3.4 Quartic in spin
10 11 12 13 13
4 Reproducing 1PM part of PN expansion 4.1 Linear in spin (up to NNNLO) 4.2 Quadratic in spin (up to NNLO) 4.3 Cubic in spin (up to NLO)
14 15 17 22
5 Effective one-body mapping
22
6 Conclusion and outlook
25
1
Introduction
The on-shell approach, characterized as exploiting kinematic constraints combined with unitarity and symmetry principles to bootstrap physical observables, has often uncovered unexpected structures hidden in conventional formalism. Indeed this has been one of the highlights in the study of scattering amplitudes for the past decade. On the other hand, as it was demonstrated long ago, (electromagnetic and) gravitational two-body potentials can be extracted from singular limits of scattering amplitudes [1–6], naturally one would expect that the hidden structures found in scattering am
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