Coordinates and boundary conditions for the general relativistic initial data problem

Using York's method, the author discusses techniques for numerically constructing GR initial data on a Cauchy surface representing spacetimes containing arbitrary numbers of black holes, each with arbitrary mass, position, (linear) momentum and spin (angular momentum). The initial data slices discussed are maximal and 3-conformally flat. The author restricts the discussion to axisymmetric asymptotically flat vacuum (outside the black holes) slices, although these restrictions are not essential.