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

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