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Suppose a small compact object (black hole or neutron star) of mass $m$orbits a large black hole of mass $M \gg m$. This system emits gravitationalwaves (GWs) that have a radiation-reaction effect on the particle's motion.EMRIs (extreme--mass-ratio inspirals) of this type will be important GW sourcesfor LISA; LISA's data analysis will require highly accurate EMRI GW templates.In this article I outline the "Capra" research program to try to model EMRIsand calculate their GWs \textit{ab initio}, assuming only that $m \ll M$ andthat the Einstein equations hold. Here we treat the EMRI spacetime as aperturbation of the large black hole's "background" (Schwarzschild or Kerr)spacetime and use the methods of black-hole perturbation theory, expanding inthe small parameter $m/M$. The small body's motion can be described either asthe result of a radiation-reaction "self-force" acting in the backgroundspacetime or as geodesic motion in a perturbed spacetime. Several differentlines of reasoning lead to the (same) basic $\O(m/M)$ "MiSaTaQuWa" equations ofmotion for the particle. Surprisingly, for a nonlinear field theory such asgeneral relativity, modelling the small body as a point particle works well.The particle's own field is singular along the particle worldline so it'sdifficult to formulate a meaningful "perturbation" theory or equations ofmotion there. I discuss "mode-sum" and "puncture-function" regularizationschemes that resolve this difficulty and allow practical self-forcecalculations, and I outline an important recent calculation of this type.  Most Capra research to date has used 1st order perturbation theory. To obtainthe very high accuracies needed to fully exploit LISA's observations of thestrongest EMRIs, 2nd order perturbation theory will probably be needed.

The Capra Research Program for Modelling Extreme Mass Ratio Inspirals