A self-force primer for numerical relativists

A small mass $\mu$ moving about a much more massive black hole $M$ travels along a world line that is most easily described as being a geodesic of the perturbed metric $g_{ab}+h_{ab}$, where $h_{ab} \sim O(\mu)$ is the metric perturbation suitably regularized at the location of the small mass. This motion is said to result from the gravitational self-force acting on $\mu$. A novel technique uses currently available methods of numerical relativity to calculate the regularized $h_{ab}$, the self-force acting back on $\mu$, and the effects of the self-force on the gravitational waves being emitted in the context of extreme mass ratio inspiral.