Multipole Analysis of Kicks in Collision of Binary Black Holes
  Thorne and Kidder give expressions which allow for analytical estimates of the "kick", it i.e. the recoil, produced from asymmetrical gravitational radiation during the interaction of black holes, or in fact any gravitating compact bodies. (The Thorne-Kidder formula uses momentum flux calculations based on the linearized General Relativity of gravitational radiation.) We specifically treat kicks arising in the binary interaction of equal mass black holes, when at least one of the black holes has significant spin, a. Such configurations can produce very large kicks in computational simulations. We consider both fly-by and quasicircular orbits. For fly-by orbits we find substantial kicks from those Thorne-Kidder terms which are linear in a. For the quasi-circular case, we consider in addition the nonlinear contribution (O(a^2)) to the kicks, and provide a dynamical explanation for such terms. However, in the cases of maximal kick velocities, the dependence on spin is largely linear (reproduced in numerical results). 
Sarah H. Miller, R.A. Matzner