Calculation of the First Nonlinear Contribution to the General-Relativistic Spin-Spin Interaction for Binary Systems

We use recently developed effective field theory techniques to calculate the third order post-Newtonian correction to the spin-spin potential between two spinning objects. This correction represents the first contribution to the spin-spin interaction due to the nonlinear nature of general relativity and will play an important role in forthcoming gravity wave experiments.

Figure 1

Diagrams contributing to 3PN order which do not involve nonlinear interactions. The blow represents a spin insertion and the cross corresponds to a propagator correction.

Figure 2

Nonlinear contributions to the 3PN spin-spin potential.