Abstract
We obtain the quadratic-in-spin terms of the conservative Hamiltonian describing the interactions of a binary of spinning bodies in General Relativity through mathcal{O} (G2) and to all orders in velocity. Our calculation extends a recently-introduced framework based on scattering amplitudes and effective field theory to consider non-minimal coupling of the spinning objects to gravity. At the order that we consider, we establish the validity of the formula proposed in [1] that relates the impulse and spin kick in a scattering event to the eikonal phase.
Highlights
This Hamiltonian was equivalent to the one of ref. [7]
The conservative Hamiltonian we obtained in the previous section enables the calculation of physical observables for a binary of compact objects interacting through gravity
In this paper we obtained the 2PM-order Hamiltonian that describes the conservative dynamics of two spinning compact objects in General Relativity up to interactions quadratic in the spin of one of the objects
Summary
We review the aspects of the higher-spin formalism that we use in the paper. We use a Lagrangian to organize the interactions of higher-spin fields with gravity. [118] obtained such a Lagrangian using auxiliary fields to eliminate all but the spin-s representation of the SO(3) rotation group We relax this requirement, and interpret the theory as a relativistic effective theory that captures all spin-induced multipole moments of spinning objects coupled to gravity. The non-minimal Lagrangian containing all the terms linear in the graviton and bilinear in the higher-spin field is. The operators in eq (2.4) are in direct correspondence to the non-minimal couplings in the worldline spinning-particle action of ref. We determine the spin connection ω as the solution of the vielbein postulate, ∇μ(ω)eνa = 0 This yields the following expansions for the needed quantities gμν = ημν + hμν , eμa δμa. Where Lq ≡ ip × q, and the ellipsis stand for terms that do not contribute to the classical potential
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