Spin-dependent post-Newtonian parameters from EMRI computation in Kerr background

Because the extreme mass-ratio inspiral (EMRI) approximation is accurate to all orders in $v/c$, it can be used to find high order post-Newtonian parameters that are not yet analytically accessible. We report here on progress in computing spin-dependent, conservative, post-Newtonian parameters from a radiation-gauge computation for a particle in circular orbit in a family of Kerr geometries. For a particle with 4-velocity $u^\alpha = U k^\alpha$, with $k^\alpha$ the helical Killing vector of the perturbed spacetime, the renormalized perturbation $\Delta U$, when written as a function of the particle's angular velocity, is invariant under gauge transformations generated by helically symmetric vectors. The EMRI computations are done in a modified radiation gauge. Extracted parameters are compared to previously known and newly computed spin-dependent post-Newtonian terms. This work is modeled on earlier computations by Blanchet, Detweiler, Le Tiec and Whiting of spin-independent terms for a particle in circular orbit in a Schwarzschild geometry.