Abstract
Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework. We introduce a systematic procedure to compute the total change in momentum and spin in the gravitational scattering of compact objects. For the special case of spins aligned with the orbital angular momentum, we show how to construct the radial action for elliptic-like orbits using the Boundary-to-Bound correspondence. As a paradigmatic example, we solve the scattering problem to next-to-leading PM order with linear and bilinear spin effects and arbitrary initial conditions, incorporating for the first time finite-size corrections. We obtain the aligned-spin radial action from the resulting scattering data, and derive the periastron advance and binding energy for circular orbits. We also provide the (square of the) center-of-mass momentum to mathcal{O}left({G}^2right) , which may be used to reconstruct a Hamiltonian. Our results are in perfect agreement with the existent literature, while at the same time extend the knowledge of the PM dynamics of compact binaries at quadratic order in spins.
Highlights
Building upon the worldline effective field theory (EFT) formalism for spinning bodies developed for the Post-Newtonian regime, we generalize the EFT approach to Post-Minkowskian (PM) dynamics to include rotational degrees of freedom in a manifestly covariant framework
The power of gravitational wave (GW) science [1] is predicated on the precise reconstruction of the GW signal as a function of the parameters of the sources, notably binary compact objects [2,3,4]
Spinning black holes have attracted interest in recent years due their ability to harvest clouds of putative ultralight particles [7], which can be fleshed out either through mass/spin distributions and GW stochastic backgrounds [8,9,10,11,12] or, more promising, the precise reconstruction of the GW signal emitted from binary systems [13, 14]
Summary
The power of gravitational wave (GW) science [1] is predicated on the precise reconstruction of the GW signal as a function of the parameters of the sources, notably binary compact objects [2,3,4]. Efforts to solve the conservative binary dynamics of compact objects have focused on the direct calculation of the Hamiltonian [68] or Lagrangian [69,70,71,72,73] as an intermedia step towards constructing waveforms This was no different for spin effects [34, 85]. While the derivation of a (classical) Hamiltonian from a (quantum) scattering amplitude as an intermedia step is a perfectly viable option (dating back to the work of Iwasaki [142]), one of the main paradigms in modern approaches is to avoid the introduction of gauge-dependent objects [89, 90] This was adopted in [96, 97] to solve the (classical) scattering problem, obtaining the impulse from the amplitude, without providing yet the necessary link to bound states.
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