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Numerical construction of space-time

Traditional analytic methods have not been powerful enough to solve for strongfield time-dependent solutions of the nonlinear Einstein field equations. For this reason, numerical solution of the equations seemed to be a natural approach. Building on the earlier work inspired by DeWitt & Misner, my colleagues and I have developed a practical algorithm for constructing space-times. The point of view is that space-time is decomposed into spacelike time slices and a congruence of curves threading these slices. The time coordinate is that scalar function which is constant on each time slice, while spatial coordinates are constant along the members of the congruence. The systematic 3+1 Hamiltonian approach was exhaustively studied by Arnowitt et al. (1962); the application to solution of the field equations was recently stressed by Smarr & York (1978 a, b).