  We present a formalism for constructing quasi-equilibrium binary black hole
initial data suitable for numerical evolution. We construct quasi-equilibrium
models by imposing an approximate helical Killing symmetry appropriate for
quasi-circular orbits. We use the sum of two Kerr-Schild metrics as our
background metric, thereby improving on conformally flat backgrounds that do
not accommodate rotating black holes and providing a horizon-penetrating lapse,
convenient for implementing black hole excision. We set inner boundary
conditions at an excision radius well inside the apparent horizon and construct
these boundary conditions to incorporate the quasi-equilibrium condition and
recover the solution for isolated black holes in the limit of large separation.
We use our formalism both to generate initial data for binary black hole
evolutions and to construct a crude quasi-equilibrium, inspiral sequence for
binary black holes of fixed irreducible mass.
