New method for solving the initial value problem with application to multiple black holes

This work consists of two distinct parts. In the first part we present a new method for solving the initial value problem of general relativity. Given any spatial metric with a surface orthogonal Killing field and two freely specified components of the extrinsic curvature, we solve for the extrinsic curvature’s remaining components. For the second part, after noting that initial data for the Kerr spacetime can be derived within our formalism, we propose data for axisymmetric configurations of spinning black holes. Though our method is limited to axisymmetry, it offers an advantage over the Bowen-York procedure that our data are designed approach those for Kerr holes in the limit of large separations and in the close limit.