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.
Highlights
A streamlined computation of spin effects in the scattering angle [20], linear and angular impulse [21] of rotating black holes, as well as new insights into the origin of shift relations between rotating and Schwarzschild black hole solutions [22]
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
We 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
Summary
The 1PM classical potential can be extracted from the singular limit of a single graviton exchange between two compact spinning objects, i.e. the 2 → 2 elastic scattering amplitude shown in figure 1. We expand in small |q|, and since in Lorentzian signature this translate to the zero momentum limit, we will analytically continuing to complex (or split signature) momenta In this case we can have |q| → 0 correspond to null momenta, q2 = 0. The associated matching procedure was introduced in [18], termed Hilbert space matching, and computed to leading PN order for each spin operator of given degree. This factor is the well known Thomas precession, for which we derive its exact form deriving the complete 1PM potential
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
