Gravitational bremsstrahlung from spinning binaries in the post-Minkowskian expansion

We present a novel calculation of the four-momentum that is radiated into gravitational waves during the scattering of two arbitrarily spinning bodies. Our result, which is accurate to leading order in $G$, to quadratic order in the spins, and to all orders in the velocity, is derived by using a Routhian-based worldline effective field theory formalism in concert with a battery of analytic techniques for evaluating loop integrals. While nonspinning binaries radiate momentum only along the direction of their relative velocity, we show that the inclusion of spins generically allows for momentum loss in all three spatial directions. We also verify that our expression for the radiated energy agrees with the overlapping terms from state-of-the-art calculations in post-Newtonian theory.

Figure 1

Feynman rules relevant to our calculation.

Figure 2

Feynman diagrams contributing to the stress-energy tensor up to next-to-leading order in $G$. While not drawn explicitly, our calculation includes the mirror inverses of (a) and (b), which are obtained by interchanging the body labels $1\leftrightarrow 2$ and redefining the loop momentum $q\mapsto k-q$.