Initial data for binary black holes in quasi-circular orbit: The conformal thin-sandwich puncture method

Numerical relativists have been trying to simulate astrophysically realistic binary black hole collisions for over fifteen years. It is believed that prior to collision the two black holes will be in a slowly decaying circular orbit. Any simulation begins with initial data, but it is not clear whether the orbits represented by current initial data for very close black holes are quasi-stable or even quasi-circular. To construct initial data we must make choices for freely-specifiable quantities and choose boundary conditions. All of these choices should be compatible with the physical system we wish to describe. The physical significance of the freely-specifiable data in York's conformal thin-sandwich (CTS) decomposition is clearer than in previous decompositions of the initial value equations of general relativity. The CTS system has already been used to construct data for quasi-equilibrium binary black hole configurations. These implementations used excision methods, which require boundary conditions on the excision surface. An alternative method that avoids inner boundary conditions is Brandt and Brügmann's puncture method. I combine the CTS decomposition and the puncture method. I show that this method is numerically feasible, but that it may not be possible to identify which of the resulting data sets represent binary black holes in quasi-circular orbits. I also consider two methods for locating quasi-circular orbits, the effective-potential and mass-comparison methods. I find that both methods agree when applied to CTT puncture initial data sets.