Abstract
Using scattering amplitudes, we obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order O(G^{4}). As in previous lower-order calculations, we harness powerful tools from the modern scattering amplitudes program including generalized unitarity, the double copy, and advanced multiloop integration methods, in combination with effective field theory. The classical amplitude involves polylogarithms with up to transcendental weight two and elliptic integrals. We derive the radial action directly from the amplitude, and determine the corresponding Hamiltonian in isotropic gauge. Our results are in agreement with known overlapping terms up to sixth post-Newtonian order, and with the probe limit. We also determine the post-Minkowskian energy loss from radiation emission at O(G^{3}) via its relation to the tail effect.
Highlights
Zvi Bern,1 Julio Parra-Martinez,2 Radu Roiban,3 Michael S
We obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order OðG4Þ
Introduction.—The emergence of gravitational-wave science [1] has dramatically underscored the scientific value of observing the Universe through an entirely new lens, and will continue to fundamentally transform key areas in astronomy, cosmology, and particle physics
Summary
Zvi Bern,1 Julio Parra-Martinez ,2 Radu Roiban,3 Michael S. Scattering Amplitudes and Conservative Binary Dynamics at OðG4Þ We obtain the potential contributions to conservative binary dynamics in general relativity at fourth post-Minkowskian order OðG4Þ.
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