Leading order finite size effects with spins for inspiralling compact binaries

TL;DR

The paper computes the leading-order finite-size effects arising from spin for inspiralling compact binaries using an EFT of gravitating spinning objects, extending the spin sector to cubic and quartic order. It introduces higher-dimensional nonminimal worldline couplings to the Weyl tensor and uses nonrelativistic gravitational fields to organize spin interactions and assemble Feynman-diagram calculations. The authors derive the complete LO cubic-in-spin potential at 3.5PN and the LO quartic-in-spin potential at 4PN for generic binaries, and fix the BH Wilson coefficients to unity by matching to gauge-invariant observables and corrected ADM results. They verify consistency with existing black-hole Hamiltonians, correct previous inaccuracies, and discuss potential universal relations among spin-induced coefficients, with future work aimed at NNLO spin-quadratic terms and EFT matching to multipole moments. These results refine the theoretical description of spin-induced finite-size effects and enhance the precision of gravitational-wave modeling for rapidly rotating binaries.

Abstract

The leading order finite size effects due to spin, namely that of the cubic and quartic in spin interactions, are derived for the first time for generic compact binaries via the effective field theory for gravitating spinning objects. These corrections enter at the third and a half and fourth post-Newtonian orders, respectively, for rapidly rotating compact objects. Hence, we complete the leading order finite size effects with spin up to the fourth post-Newtonian accuracy. We arrive at this by augmenting the point particle effective action with new higher dimensional nonminimal coupling worldline operators, involving higher-order derivatives of the gravitational field, and introducing new Wilson coefficients, corresponding to constants, which describe the octupole and hexadecapole deformations of the object due to spin. These Wilson coefficients are fixed to unity in the black hole case. The nonminimal coupling worldline operators enter the action with the electric and magnetic components of the Weyl tensor of even and odd parity, coupled to even and odd worldline spin tensors, respectively. Moreover, the non relativistic gravitational field decomposition, which we employ, demonstrates a coupling hierarchy of the gravito-magnetic vector and the Newtonian scalar, to the odd and even in spin operators, respectively, which extends that of minimal coupling. This observation is useful for the construction of the Feynman diagrams, and provides an instructive analogy between the leading order spin-orbit and cubic in spin interactions, and between the leading order quadratic and quartic in spin interactions.

Figures (3)

• Figure 1: LO spin-squared interaction Feynman diagram. This diagram should be included together with its mirror image. This is a quadrupole-monopole interaction. Note the analogy with the Newtonian interaction.
• Figure 2: LO cubic in spin interaction Feynman diagrams. These diagrams should be included together with their mirror images. On the left pair we have the quadrupole-dipole interaction, and on the right pair we have the octupole-monopole one. Note the analogy of each pair with the LO spin-orbit interaction in figure 1 of Levi:2010zu.
• Figure 3: LO quartic in spin interaction Feynman diagrams. Diagrams b and c here should be included together with their mirror images. On the left and right we have the quadrupole-quadrupole and hexadecapole-monopole interactions, each of which is analogous to the LO spin-squared interaction in figure 1 here. On the middle we have the octupole-dipole interaction analogous to the LO spin1-spin2 interaction in figure 1 of Levi:2008nh.