Time-asymmetric initial data for the N black hole problem in general relativity

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Abstract
The time‐asymmetric initial‐value problem for N‐body systems consisting of N black holes is described. The spacelike hypersurface for setting up the initial data is chosen to be the Einstein–Rosen manifold with N bridges. An explicit procedure in the form of an infinite series is given to construct solutions of the momentum constraints on the Einstein–Rosen manifold, starting from any solution of the momentum constraints in three‐dimensional Euclidean space. A sufficient condition for the absolute convergence of a wide range of these solutions is derived. In particular, the solution representing N black holes with arbitrary momenta and spins is presented. The formulation of the Hamiltonian constraint as a boundary‐value problem is discussed briefly.