Quasi-stationary binary inspiral: II. Radiation-balanced boundary conditions

The quasi-stationary method for black hole binary inspiral is an approximat ion for studying strong-field effects while suppressing radiation reaction. In this paper we use a nonlinear scalar field toy model to: (a) explain th e underlying method of approximating binary motion by periodic orbits with radiation; (b) show how the fields in such a model are found by the solutio n of a boundary value problem; (c) demonstrate how a good approximation to the outgoing radiation can be found by finding fields with a balance of ing oing and outgoing radiation (a generalization of standing waves).