Corotating and irrotational binary black holes in quasicircular orbits

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Abstract
A complete formalism for constructing initial data representing black-hole binaries in quasi-equilibrium is developed. Radiation reaction prohibits, in general, true equilibrium binary configurations. However, when the time scale for orbital decay is much longer than the orbital period, a binary can be considered to be in quasiequilibrium. If each black hole is assumed to be in quasiequilibrium, then a complete set of boundary conditions for all initial data variables can be developed. These boundary conditions are applied on the apparent horizon of each black hole, and in fact force a specified surface to be an apparent horizon. A global assumption of quasiequilibrium is also used to fix some of the freely specifiable pieces of the initial data and to uniquely fix the asymptotic boundary conditions. This formalism should allow for the construction of completely general quasiequilibrium black hole binary initial data.