High Velocity Collision of Two Blackholes: initial Data

Larry Smarr and B. S. Dewitt, Univ. of Texas at Austin–As a first step toward finding the spacetime development of two colliding black holes, one needs to pose realistic initial data. We report progress toward numerical calculation of maximal (but non-time symmetric) initial value spacelike hypersurfaces which represent two black holes colliding head-on with arbitrary closing velocity. The solution is obtained by “adding” two 3-metrics and then, following a suggestion by J.W. York*, conformally mapping this sum onto a 3-geometry, which satisfies the constraint equations. Each of the 3-metrics to be added is a maximal slice of Schwarzschild which becomes asymptotic to boosted t=constant slices.

*J.W. York, Jr. “Conformally Invariant Orthogonal Decomposition of Symmetric Tensors on Riemannian Manifolds and the Initial Value Problem of General Relativity,” Princeton Univ. Preprint (1972).